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3D Geometry

434 Questions
All Exams JEE Mains JEE Advanced
2019 JEE Mains MCQ
JEE Main 2019 (Online) 12th April Evening Slot
The length of the perpendicular drawn from the point (2, 1, 4) to the plane containing the lines
$\overrightarrow r = \left( {\widehat i + \widehat j} \right) + \lambda \left( {\widehat i + 2\widehat j - \widehat k} \right)$ and $\overrightarrow r = \left( {\widehat i + \widehat j} \right) + \mu \left( { - \widehat i + \widehat j - 2\widehat k} \right)$ is :
A.
${1 \over 3}$
B.
${1 \over {\sqrt 3 }}$
C.
3
D.
${\sqrt 3 }$
2019 JEE Mains MCQ
JEE Main 2019 (Online) 12th April Evening Slot
A plane which bisects the angle between the two given planes 2x – y + 2z – 4 = 0 and x + 2y + 2z – 2 = 0, passes through the point :
A.
(1, –4, 1)
B.
(1, 4, –1)
C.
(2, 4, 1)
D.
(2, –4, 1)
2019 JEE Mains MCQ
JEE Main 2019 (Online) 12th April Morning Slot
If the line ${{x - 2} \over 3} = {{y + 1} \over 2} = {{z - 1} \over { - 1}}$ intersects the plane 2x + 3y – z + 13 = 0 at a point P and the plane 3x + y + 4z = 16 at a point Q, then PQ is equal to :
A.
$2\sqrt 7 $
B.
14
C.
$2\sqrt {14} $
D.
$\sqrt {14} $
2019 JEE Mains MCQ
JEE Main 2019 (Online) 10th April Evening Slot
A perpendicular is drawn from a point on the line ${{x - 1} \over 2} = {{y + 1} \over { - 1}} = {z \over 1}$ to the plane x + y + z = 3 such that the foot of the perpendicular Q also lies on the plane x – y + z = 3. Then the co-ordinates of Q are :
A.
(4, 0, – 1)
B.
(2, 0, 1)
C.
(1, 0, 2)
D.
(– 1, 0, 4)
2019 JEE Mains MCQ
JEE Main 2019 (Online) 10th April Evening Slot
If the plane 2x – y + 2z + 3 = 0 has the distances ${1 \over 3}$ and ${2 \over 3}$ units from the planes 4x – 2y + 4z + $\lambda $ = 0 and 2x – y + 2z + $\mu $ = 0, respectively, then the maximum value of $\lambda $ + $\mu $ is equal to :
A.
13
B.
9
C.
5
D.
15
2019 JEE Mains MCQ
JEE Main 2019 (Online) 10th April Morning Slot
If the length of the perpendicular from the point ($\beta $, 0, $\beta $) ($\beta $ $ \ne $ 0) to the line,
${x \over 1} = {{y - 1} \over 0} = {{z + 1} \over { - 1}}$ is $\sqrt {{3 \over 2}} $, then $\beta $ is equal to :
A.
2
B.
1
C.
-2
D.
-1
2019 JEE Mains MCQ
JEE Main 2019 (Online) 10th April Morning Slot
If Q(0, –1, –3) is the image of the point P in the plane 3x – y + 4z = 2 and R is the point (3, –1, –2), then the area (in sq. units) of $\Delta $PQR is :
A.
${{\sqrt {65} } \over 2}$
B.
$2\sqrt {13} $
C.
${{\sqrt {91} } \over 2}$
D.
${{\sqrt {91} } \over 4}$
2019 JEE Mains MCQ
JEE Main 2019 (Online) 9th April Evening Slot
The vertices B and C of a $\Delta $ABC lie on the line,

${{x + 2} \over 3} = {{y - 1} \over 0} = {z \over 4}$ such that BC = 5 units.

Then the area (in sq. units) of this triangle, given that the point A(1, –1, 2), is :
A.
6
B.
$5\sqrt {17} $
C.
$\sqrt {34} $
D.
$2\sqrt {34} $
2019 JEE Mains MCQ
JEE Main 2019 (Online) 9th April Evening Slot
Let P be the plane, which contains the line of intersection of the planes, x + y + z – 6 = 0 and 2x + 3y + z + 5 = 0 and it is perpendicular to the xy-plane. Then the distance of the point (0, 0, 256) from P is equal to :
A.
205$\sqrt5$
B.
63$\sqrt5$
C.
11/$\sqrt5$
D.
17/$\sqrt5$
2019 JEE Mains MCQ
JEE Main 2019 (Online) 9th April Morning Slot
A plane passing through the points (0, –1, 0) and (0, 0, 1) and making an angle ${\pi \over 4}$ with the plane y – z + 5 = 0, also passes through the point
A.
$\left( {\sqrt 2 ,1,4} \right)$
B.
$\left(- {\sqrt 2 ,1,4} \right)$
C.
$\left( -{\sqrt 2 ,-1,-4} \right)$
D.
$\left( {\sqrt 2 ,-1,4} \right)$
2019 JEE Mains MCQ
JEE Main 2019 (Online) 9th April Morning Slot
If the line, ${{x - 1} \over 2} = {{y + 1} \over 3} = {{z - 2} \over 4}$ meets the plane, x + 2y + 3z = 15 at a point P, then the distance of P from the origin is :
A.
${{\sqrt 5 } \over 2}$
B.
2$\sqrt 5$
C.
9/2
D.
7/2
2019 JEE Mains MCQ
JEE Main 2019 (Online) 8th April Evening Slot
If a point R(4, y, z) lies on the line segment joining the points P(2, –3, 4) and Q(8, 0, 10), then the distance of R from the origin is :
A.
$2 \sqrt {14}$
B.
$ \sqrt {53}$
C.
$2 \sqrt {21}$
D.
6
2019 JEE Mains MCQ
JEE Main 2019 (Online) 8th April Evening Slot
The vector equation of the plane through the line of intersection of the planes x + y + z = 1 and 2x + 3y+ 4z = 5 which is perpendicular to the plane x – y + z = 0 is :
A.
$\mathop r\limits^ \to \times \left( {\mathop i\limits^ \wedge - \mathop k\limits^ \wedge } \right) - 2 = 0$
B.
$\mathop r\limits^ \to . \left( {\mathop i\limits^ \wedge + \mathop k\limits^ \wedge } \right) + 2 = 0$
C.
$\mathop r\limits^ \to . \left( {\mathop i\limits^ \wedge - \mathop k\limits^ \wedge } \right) + 2 = 0$
D.
$\mathop r\limits^ \to \times \left( {\mathop i\limits^ \wedge - \mathop k\limits^ \wedge } \right) + 2 = 0$
2019 JEE Mains MCQ
JEE Main 2019 (Online) 8th April Morning Slot
The magnitude of the projection of the vector $\mathop {2i}\limits^ \wedge + \mathop {3j}\limits^ \wedge + \mathop k\limits^ \wedge $ on the vector perpendicular to the plane containing the vectors $\mathop {i}\limits^ \wedge + \mathop {j}\limits^ \wedge + \mathop k\limits^ \wedge $ and $\mathop {i}\limits^ \wedge + \mathop {2j}\limits^ \wedge + \mathop {3k}\limits^ \wedge $ , is :
A.
${{\sqrt 3 } \over 2}$
B.
$\sqrt 6 $
C.
$\sqrt {3 \over 2} $
D.
3$\sqrt 6 $
2019 JEE Mains MCQ
JEE Main 2019 (Online) 8th April Morning Slot
The equation of a plane containing the line of intersection of the planes 2x – y – 4 = 0 and y + 2z – 4 = 0 and passing through the point (1, 1, 0) is :
A.
x – 3y – 2z = –2
B.
2x – z = 2
C.
x – y – z = 0
D.
x + 3y + z = 4
2019 JEE Mains MCQ
JEE Main 2019 (Online) 8th April Morning Slot
The length of the perpendicular from the point (2, –1, 4) on the straight line,

${{x + 3} \over {10}}$= ${{y - 2} \over {-7}}$ = ${{z} \over {1}}$ is :
A.
less than 2
B.
greater than 4
C.
greater than 2 but less than 3
D.
greater than 3 but less than 4
2019 JEE Mains MCQ
JEE Main 2019 (Online) 12th January Evening Slot
Let S be the set of all real values of $\lambda $ such that a plane passing through the points (–$\lambda $2, 1, 1), (1, –$\lambda $2, 1) and (1, 1, – $\lambda $2) also passes through the point (–1, –1, 1). Then S is equal to :
A.
{1, $-$1}
B.
{3, $-$ 3}
C.
$\left\{ {\sqrt 3 } \right\}$
D.
$\left\{ {\sqrt 3 , - \sqrt 3 } \right\}$
2019 JEE Mains MCQ
JEE Main 2019 (Online) 12th January Evening Slot
If an angle between the line, ${{x + 1} \over 2} = {{y - 2} \over 1} = {{z - 3} \over { - 2}}$ and the plane, $x - 2y - kz = 3$ is ${\cos ^{ - 1}}\left( {{{2\sqrt 2 } \over 3}} \right),$ then a value of k is :
A.
$\sqrt {{3 \over 5}} $
B.
$ - {5 \over 2}$
C.
$ - {3 \over 2}$
D.
$\sqrt {{5 \over 3}} $
2019 JEE Mains MCQ
JEE Main 2019 (Online) 12th January Morning Slot
The perpendicular distance from the origin to the plane containing the two lines,

${{x + 2} \over 3} = {{y - 2} \over 5} = {{z + 5} \over 7}$ and

${{x - 1} \over 1} = {{y - 4} \over 4} = {{z + 4} \over 7},$ is :
A.
$6\sqrt {11} $
B.
${{11} \over {\sqrt 6 }}$
C.
11
D.
11$\sqrt 6 $
2019 JEE Mains MCQ
JEE Main 2019 (Online) 12th January Morning Slot
A tetrahedron has vertices P(1, 2, 1), Q(2, 1, 3), R(–1, 1, 2) and O(0, 0, 0). The angle between the faces OPQ and PQR is :
A.
cos$-$1$\left( {{{17} \over {31}}} \right)$
B.
cos$-$1$\left( {{{9} \over {35}}} \right)$
C.
cos$-$1$\left( {{{19} \over {35}}} \right)$
D.
cos$-$1$\left( {{7 \over {31}}} \right)$
2019 JEE Mains MCQ
JEE Main 2019 (Online) 11th January Evening Slot
Two lines ${{x - 3} \over 1} = {{y + 1} \over 3} = {{z - 6} \over { - 1}}$ and ${{x + 5} \over 7} = {{y - 2} \over { - 6}} = {{z - 3} \over 4}$ intersect at the point R. The reflection of R in the xy-plane has coordinates :
A.
(2, 4, 7)
B.
(2, $-$ 4, $-$7)
C.
(2, $-$ 4, 7)
D.
($-$ 2, 4, 7)
2019 JEE Mains MCQ
JEE Main 2019 (Online) 11th January Evening Slot
If the point (2, $\alpha $, $\beta $) lies on the plane which passes through the points (3, 4, 2) and (7, 0, 6) and is perpendicular to the plane 2x – 5y = 15, then 2$\alpha $ – 3$\beta $ is equal to
A.
12
B.
7
C.
17
D.
5
2019 JEE Mains MCQ
JEE Main 2019 (Online) 11th January Morning Slot
The plane containing the line ${{x - 3} \over 2} = {{y + 2} \over { - 1}} = {{z - 1} \over 3}$ and also containing its projection on the plane 2x + 3y $-$ z = 5, contains which one of the following points ?
A.
($-$ 2, 2, 2)
B.
(2, 2, 0)
C.
(2, 0, $-$ 2)
D.
(0, $-$ 2, 2)
2019 JEE Mains MCQ
JEE Main 2019 (Online) 11th January Morning Slot
The direction ratios of normal to the plane through the points (0, –1, 0) and (0, 0, 1) and making an angle ${\pi \over 4}$ with the plane y $-$ z + 5 = 0 are :
A.
2, $-$1, 1
B.
$2\sqrt 3 ,1, - 1$
C.
$\sqrt 2 ,1, - 1$
D.
$\sqrt 2 , - \sqrt 2 $
2019 JEE Mains MCQ
JEE Main 2019 (Online) 10th January Evening Slot
On which of the following lines lies the point of intersection of the line,   ${{x - 4} \over 2} = {{y - 5} \over 2} = {{z - 3} \over 1}$  and the plane, x + y + z = 2 ?
A.
${{x - 4} \over 1} = {{y - 5} \over 1} = {{z - 5} \over { - 1}}$
B.
${{x - 2} \over 2} = {{y - 3} \over 2} = {{z + 3} \over 3}$
C.
${{x - 1} \over 1} = {{y - 3} \over 2} = {{z + 4} \over { - 5}}$
D.
${{x + 3} \over 3} = {{4 - y} \over 3} = {{z + 1} \over { - 2}}$
2019 JEE Mains MCQ
JEE Main 2019 (Online) 10th January Evening Slot
The plane which bisects the line segment joining the points (–3, –3, 4) and (3, 7, 6) at right angles, passes through which one of the following points ?
A.
(2, 1, 3)
B.
(4, $-$ 1, 2)
C.
(4, 1, $-$ 2)
D.
($-$ 2, 3, 5)
2019 JEE Mains MCQ
JEE Main 2019 (Online) 10th January Morning Slot
The plane passing through the point (4, –1, 2) and parallel to the lines  ${{x + 2} \over 3} = {{y - 2} \over { - 1}} = {{z + 1} \over 2}$  and  ${{x - 2} \over 1} = {{y - 3} \over 2} = {{z - 4} \over 3}$ also passes through the point -
A.
(1, 1, $-$ 1)
B.
(1, 1, 1)
C.
($-$ 1, $-$ 1, $-$1)
D.
($-$ 1, $-$ 1, 1)
2019 JEE Mains MCQ
JEE Main 2019 (Online) 10th January Morning Slot
Let A be a point on the line $\overrightarrow r = \left( {1 - 3\mu } \right)\widehat i + \left( {\mu - 1} \right)\widehat j + \left( {2 + 5\mu } \right)\widehat k$ and B(3, 2, 6) be a point in the space. Then the value of $\mu $ for which the vector $\overrightarrow {AB} $  is parallel to the plane x $-$ 4y + 3z = 1 is -
A.
${1 \over 8}$
B.
${1 \over 2}$
C.
${1 \over 4}$
D.
$-$ ${1 \over 4}$
2019 JEE Mains MCQ
JEE Main 2019 (Online) 9th January Evening Slot
The equation of the plane containing the straight line ${x \over 2} = {y \over 3} = {z \over 4}$ and perpendicular to the plane containing the straight lines ${x \over 3} = {y \over 4} = {z \over 2}$ and ${x \over 4} = {y \over 2} = {z \over 3}$ is :
A.
x $-$ 2y + z = 0
B.
3x + 2y $-$ 3z = 0
C.
x + 2y $-$ 2z = 0
D.
5x + 2y $-$ 4z = 0
2019 JEE Mains MCQ
JEE Main 2019 (Online) 9th January Evening Slot
If the lines x = ay + b, z = cy + d and x = a'z + b', y = c'z + d' are perpendicular, then :
A.
ab'  +  bc'  +  1  =  0
B.
cc'  +  a   +  a'  =  0
C.
bb'  +  cc'  +  1  =  0
D.
aa'  +  c  +  c'  =  0
2019 JEE Mains MCQ
JEE Main 2019 (Online) 9th January Morning Slot
The plane through the intersection of the planes x + y + z = 1 and 2x + 3y – z + 4 = 0 and parallel to y-axis also passes through the point :
A.
(–3, 0, -1)
B.
(3, 2, 1)
C.
(3, 3, -1)
D.
(–3, 1, 1)
2019 JEE Mains MCQ
JEE Main 2019 (Online) 9th January Morning Slot
The equation of the line passing through (–4, 3, 1), parallel

to the plane x + 2y – z – 5 = 0 and intersecting

the line ${{x + 1} \over { - 3}} = {{y - 3} \over 2} = {{z - 2} \over { - 1}}$ is :
A.
${{x + 4} \over 3} = {{y - 3} \over {-1}} = {{z - 1} \over 1}$
B.
${{x + 4} \over 1} = {{y - 3} \over {1}} = {{z - 1} \over 3}$
C.
${{x + 4} \over -1} = {{y - 3} \over {1}} = {{z - 1} \over 1}$
D.
${{x - 4} \over 2} = {{y + 3} \over {1}} = {{z + 1} \over 4}$
2018 JEE Mains MCQ
JEE Main 2018 (Online) 16th April Morning Slot
The sum of the intercepts on the coordinate axes of the plane passing through the point ($-$2, $-2,$ 2) and containing the line joining the points (1, $-$1, 2) and (1, 1, 1) is :
A.
4
B.
$-$ 4
C.
$-$ 8
D.
12
2018 JEE Mains MCQ
JEE Main 2018 (Online) 16th April Morning Slot
If the angle between the lines, ${x \over 2} = {y \over 2} = {z \over 1}$

and ${{5 - x} \over { - 2}} = {{7y - 14} \over p} = {{z - 3} \over 4}\,\,$ is ${\cos ^{ - 1}}\left( {{2 \over 3}} \right),$ then p is equal to :
A.
${7 \over 2}$
B.
${2 \over 7}$
C.
$-$ ${7 \over 4}$
D.
$-$ ${4 \over 7}$
2018 JEE Mains MCQ
JEE Main 2018 (Offline)
The length of the projection of the line segment joining the points (5, -1, 4) and (4, -1, 3) on the plane, x + y + z = 7 is :
A.
$\sqrt {{2 \over 3}} $
B.
${2 \over {\sqrt 3 }}$
C.
${2 \over 3}$
D.
${1 \over 3}$
2018 JEE Mains MCQ
JEE Main 2018 (Offline)
If L1 is the line of intersection of the planes 2x - 2y + 3z - 2 = 0, x - y + z + 1 = 0 and L2 is the line of intersection of the planes x + 2y - z - 3 = 0, 3x - y + 2z - 1 = 0, then the distance of the origin from the plane, containing the lines L1 and L2, is :
A.
${1 \over {\sqrt 2 }}$
B.
${1 \over {4\sqrt 2 }}$
C.
${1 \over {3\sqrt 2 }}$
D.
${1 \over {2\sqrt 2 }}$
2018 JEE Mains MCQ
JEE Main 2018 (Online) 15th April Evening Slot
An angle between the lines whose direction cosines are gien by the equations,
$l$ + 3m + 5n = 0 and 5$l$m $-$ 2mn + 6n$l$ = 0, is :
A.
${\cos ^{ - 1}}\left( {{1 \over 3}} \right)$
B.
${\cos ^{ - 1}}\left( {{1 \over 4}} \right)$
C.
${\cos ^{ - 1}}\left( {{1 \over 6}} \right)$
D.
${\cos ^{ - 1}}\left( {{1 \over 8}} \right)$
2018 JEE Mains MCQ
JEE Main 2018 (Online) 15th April Evening Slot
A plane bisects the line segment joining the points (1, 2, 3) and ($-$ 3, 4, 5) at rigt angles. Then this plane also passes through the point :
A.
($-$ 3, 2, 1)
B.
(3, 2, 1)
C.
($-$ 1, 2, 3)
D.
(1, 2, $-$ 3)
2018 JEE Mains MCQ
JEE Main 2018 (Online) 15th April Morning Slot
A variable plane passes through a fixed point (3,2,1) and meets x, y and z axes at A, B and C respectively. A plane is drawn parallel to yz -plane through A, a second plane is drawn parallel zx-plane through B and a third plane is drawn parallel to xy-plane through C. Then the locus of the point of intersection of these three planes, is :
A.
${x \over 3} + {y \over 2} + {z \over 1} = 1$
B.
x + y + z = 6
C.
${1 \over x} + {1 \over y} + {1 \over z} = {{11} \over 6}$
D.
${3 \over x} + {2 \over y} + {1 \over z} = 1$
2018 JEE Mains MCQ
JEE Main 2018 (Online) 15th April Morning Slot
An angle between the plane, x + y + z = 5 and the line of intersection of the planes, 3x + 4y + z $-$ 1 = 0 and 5x + 8y + 2z + 14 =0, is :
A.
${\sin ^{ - 1}}\left( {\sqrt {{\raise0.5ex\hbox{$\scriptstyle 3$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle {17}$}}} } \right)$
B.
${\cos ^{ - 1}}\left( {\sqrt {{\raise0.5ex\hbox{$\scriptstyle 3$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle {17}$}}} } \right)$
C.
${\cos ^{ - 1}}\left( {{\raise0.5ex\hbox{$\scriptstyle 3$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle {17}$}}} \right)$
D.
${\sin ^{ - 1}}\left( {{\raise0.5ex\hbox{$\scriptstyle 3$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle {17}$}}} \right)$
2017 JEE Mains MCQ
JEE Main 2017 (Online) 9th April Morning Slot
If a variable plane, at a distance of 3 units from the origin, intersects the coordinate axes at A, B and C, then the locus of the centroid of $\Delta $ABC is :
A.
${1 \over {{x^2}}} + {1 \over {{y^2}}} + {1 \over {{z^2}}} = 1$
B.
${1 \over {{x^2}}} + {1 \over {{y^2}}} + {1 \over {{z^2}}} = 3$
C.
${1 \over {{x^2}}} + {1 \over {{y^2}}} + {1 \over {{z^2}}} = {1 \over 9}$
D.
${1 \over {{x^2}}} + {1 \over {{y^2}}} + {1 \over {{z^2}}} = 9$
2017 JEE Mains MCQ
JEE Main 2017 (Online) 9th April Morning Slot
If the line, ${{x - 3} \over 1} = {{y + 2} \over { - 1}} = {{z + \lambda } \over { - 2}}$ lies in the plane, 2x−4y+3z=2, then the shortest distance between this line and the line, ${{x - 1} \over {12}} = {y \over 9} = {z \over 4}$ is :
A.
2
B.
1
C.
0
D.
3
2017 JEE Mains MCQ
JEE Main 2017 (Online) 9th April Morning Slot
If x = a, y = b, z = c is a solution of the system of linear equations

x + 8y + 7z = 0

9x + 2y + 3z = 0

x + y + z = 0

such that the point (a, b, c) lies on the plane x + 2y + z = 6, then 2a + b + c equals :
A.
$-$ 1
B.
0
C.
1
D.
2
2017 JEE Mains MCQ
JEE Main 2017 (Online) 8th April Morning Slot
The line of intersection of the planes $\overrightarrow r .\left( {3\widehat i - \widehat j + \widehat k} \right) = 1\,\,$ and
$\overrightarrow r .\left( {\widehat i + 4\widehat j - 2\widehat k} \right) = 2,$ is :
A.
${{x - {4 \over 7}} \over { - 2}} = {y \over 7} = {{z - {5 \over 7}} \over {13}}$
B.
${{x - {4 \over 7}} \over 2} = {y \over { - 7}} = {{z + {5 \over 7}} \over {13}}$
C.
${{x - {6 \over {13}}} \over 2} = {{y - {5 \over {13}}} \over { - 7}} = {z \over { - 13}}$
D.
${{x - {6 \over {13}}} \over 2} = {{y - {5 \over {13}}} \over 7} = {z \over { - 13}}$
2017 JEE Mains MCQ
JEE Main 2017 (Online) 8th April Morning Slot
The coordinates of the foot of the perpendicular from the point (1, $-$2, 1) on the plane containing the lines, ${{x + 1} \over 6} = {{y - 1} \over 7} = {{z - 3} \over 8}$ and ${{x - 1} \over 3} = {{y - 2} \over 5} = {{z - 3} \over 7},$ is :
A.
(2, $-$4, 2)
B.
($-$ 1, 2, $-$1)
C.
(0, 0, 0)
D.
(1, 1, 1)
2017 JEE Mains MCQ
JEE Main 2017 (Offline)
The distance of the point (1, 3, – 7) from the plane passing through the point (1, –1, – 1), having normal perpendicular to both the lines

${{x - 1} \over 1} = {{y + 2} \over { - 2}} = {{z - 4} \over 3}$

and

${{x - 2} \over 2} = {{y + 1} \over { - 1}} = {{z + 7} \over { - 1}}$ is :
A.
${{10} \over {\sqrt {83} }}$
B.
${{5} \over {\sqrt {83} }}$
C.
${{10} \over {\sqrt {74} }}$
D.
${{20} \over {\sqrt {74} }}$
2017 JEE Mains MCQ
JEE Main 2017 (Offline)
If the image of the point P(1, –2, 3) in the plane, 2x + 3y – 4z + 22 = 0 measured parallel to the line,

${x \over 1} = {y \over 4} = {z \over 5}$ is Q, then PQ is equal to:
A.
$2\sqrt {42} $
B.
$\sqrt {42} $
C.
$6\sqrt 5 $
D.
$3\sqrt 5 $
2016 JEE Mains MCQ
JEE Main 2016 (Online) 10th April Morning Slot
The number of distinct real values of $\lambda $ for which the lines

${{x - 1} \over 1} = {{y - 2} \over 2} = {{z + 3} \over {{\lambda ^2}}}$ and ${{x - 3} \over 1} = {{y - 2} \over {{\lambda ^2}}} = {{z - 1} \over 2}$ are coplanar is :
A.
4
B.
1
C.
2
D.
3
2016 JEE Mains MCQ
JEE Main 2016 (Online) 10th April Morning Slot
ABC is a triangle in a plane with vertices

A(2, 3, 5), B(−1, 3, 2) and C($\lambda $, 5, $\mu $).

If the median through A is equally inclined to the coordinate axes, then the value of ($\lambda $3 + $\mu $3 + 5) is :
A.
1130
B.
1348
C.
676
D.
1077
2016 JEE Mains MCQ
JEE Main 2016 (Online) 9th April Morning Slot
The shortest distance between the lines ${x \over 2} = {y \over 2} = {z \over 1}$ and
${{x + 2} \over { - 1}} = {{y - 4} \over 8} = {{z - 5} \over 4}$ lies in the interval :
A.
[0, 1)
B.
[1, 2)
C.
(2,  3]
D.
(3, 4]