← Back to Mathematics

3D Geometry

390 Questions Start JEE Mains Test
All Exams JEE Mains JEE Advanced TS-EAMCET AP-EAPCET BITSAT
2016 Q351 JEE Mains MCQ
14 Mar 2026
The distance of the point $(1,-5,9)$ from the plane $x-y+z=5$ measured along the line $x=y=z$ is :
A.
${{10} \over {\sqrt 3 }}$
B.
${20 \over 3}$
C.
$3\sqrt {10} $
D.
$10\sqrt {3} $
2016 Q352 JEE Mains MCQ
14 Mar 2026
If the line, ${{x - 3} \over 2} = {{y + 2} \over { - 1}} = {{z + 4} \over 3}\,$ lies in the planes, $lx+my-z=9,$ then ${l^2} + {m^2}$ is equal to :
A.
$5$
B.
$2$
C.
$26$
D.
$18$
2015 Q353 JEE Mains MCQ
14 Mar 2026
The distance of the point $(1, 0, 2)$ from the point of intersection of the line ${{x - 2} \over 3} = {{y + 1} \over 4} = {{z - 2} \over {12}}$ and the plane $x - y + z = 16,$ is :
A.
$3\sqrt {21} $
B.
$13$
C.
$2\sqrt {14} $
D.
$8$
2015 Q354 JEE Mains MCQ
14 Mar 2026
The equation of the plane containing the line $2x-5y+z=3; x+y+4z=5,$ and parallel to the plane, $x+3y+6z=1,$ is :
A.
$x+3y+6z=7$
B.
$2x+6y+12z=-13$
C.
$2x+6y+12z=13$
D.
$x+3y+6z=-7$
2014 Q355 JEE Mains MCQ
14 Mar 2026
The image of the line ${{x - 1} \over 3} = {{y - 3} \over 1} = {{z - 4} \over { - 5}}\,$ in the plane $2x-y+z+3=0$ is the line :
A.
${{x - 3} \over 3} = {{y + 5} \over 1} = {{z - 2} \over { - 5}}$
B.
${{x - 3} \over { - 3}} = {{y + 5} \over { - 1}} = {{z - 2} \over 5}\,$
C.
${{x + 3} \over 3} = {{y - 5} \over 1} = {{z - 2} \over { - 5}}\,$
D.
${{x + 3} \over { - 3}} = {{y - 5} \over { - 1}} = {{z + 2} \over 5}$
2014 Q356 JEE Mains MCQ
14 Mar 2026
The angle between the lines whose direction cosines satisfy the equations $l+m+n=0$ and ${l^2} = {m^2} + {n^2}$ is :
A.
${\pi \over 6}$
B.
${\pi \over 2}$
C.
${\pi \over 3}$
D.
${\pi \over 4}$
2013 Q357 JEE Mains MCQ
14 Mar 2026
If the lines ${{x - 2} \over 1} = {{y - 3} \over 1} = {{z - 4} \over { - k}}$ and ${{x - 1} \over k} = {{y - 4} \over 2} = {{z - 5} \over 1}$ are coplanar, then $k$ can have :
A.
any value
B.
exactly one value
C.
exactly two values
D.
exactly three values
2013 Q358 JEE Mains MCQ
14 Mar 2026
Distance between two parallel planes $2x+y+2z=8$ and $4x+2y+4z+5=0$ is :
A.
${3 \over 2}$
B.
${5 \over 2}$
C.
${7 \over 2}$
D.
${9 \over 2}$
2012 Q359 JEE Mains MCQ
14 Mar 2026
If the line ${{x - 1} \over 2} = {{y + 1} \over 3} = {{z - 1} \over 4}$ and ${{x - 3} \over 1} = {{y - k} \over 2} = {z \over 1}$ intersect, then $k$ is equal to :
A.
$-1$
B.
${2 \over 9}$
C.
${9 \over 2}$
D.
$0$
2012 Q360 JEE Mains MCQ
14 Mar 2026
A equation of a plane parallel to the plane $x-2y+2z-5=0$ and at a unit distance from the origin is :
A.
$x-2y+2z-3=0$
B.
$x-2y+2z+1=0$
C.
$x-2y+2z-1=0$
D.
$x-2y+2z+5=0$
2011 Q361 JEE Mains MCQ
14 Mar 2026
If the angle between the line $x = {{y - 1} \over 2} = {{z - 3} \over \lambda }$ and the plane

$x+2y+3z=4$ is ${\cos ^{ - 1}}\left( {\sqrt {{5 \over {14}}} } \right),$ then $\lambda $ equals :
A.
${3 \over 2}$
B.
${2 \over 5}$
C.
${5 \over 3}$
D.
${2 \over 3}$
2011 Q362 JEE Mains MCQ
14 Mar 2026
Statement - 1 : The point $A(1,0,7)$ is the mirror image of the point

$B(1,6,3)$ in the line : ${x \over 1} = {{y - 1} \over 2} = {{z - 2} \over 3}$

Statement - 2 : The line ${x \over 1} = {{y - 1} \over 2} = {{z - 2} \over 3}$ bisects the line

segment joining $A(1,0,7)$ and $B(1, 6, 3)$
A.
Statement -1 is true, Statement -2 is true; Statement -2 is not a correct explanation for Statement -1.
B.
Statement -1 is true, Statement - 2 is false.
C.
Statement - 1 is false , Statement -2 is true.
D.
Statement -1 is true, Statement -2 is true; Statement -2 is a correct explanation for Statement -1.
2010 Q363 JEE Mains MCQ
14 Mar 2026
A line $AB$ in three-dimensional space makes angles ${45^ \circ }$ and ${120^ \circ }$ with the positive $x$-axis and the positive $y$-axis respectively. If $AB$ makes an acute angle $\theta $ with the positive $z$-axis, then $\theta $ equals :
A.
${45^ \circ }$
B.
${60^ \circ }$
C.
${75^ \circ }$
D.
${30^ \circ }$
2010 Q364 JEE Mains MCQ
14 Mar 2026
Statement-1 : The point $A(3, 1, 6)$ is the mirror image of the point $B(1, 3, 4)$ in the plane $x-y+z=5.$

Statement-2 : The plane $x-y+z=5$ bisects the line segment joining $A(3, 1, 6)$ and $B(1, 3, 4).$
A.
Statement - 1 is true, Statement - 2 is true; Statement - 2 is not a correct explanation for Statement - 1.
B.
Statement - 1 is true, Statement - 2 is false.
C.
Statement - 1 is false , Statement - 2 is true.
D.
Statement - 1 is true, Statement - 2 is true; Statement - 2 is a correct explanation for Statement - 1.
2009 Q365 JEE Mains MCQ
14 Mar 2026
Let the line $\,\,\,\,\,$ ${{x - 2} \over 3} = {{y - 1} \over { - 5}} = {{z + 2} \over 2}$ lie in the plane $\,\,\,\,\,$ $x + 3y - \alpha z + \beta = 0.$ Then $\left( {\alpha ,\beta } \right)$ equals
A.
$(-6,7)$
B.
$(5,-15)$
C.
$(-5,5)$
D.
$(6, -17)$
2009 Q366 JEE Mains MCQ
14 Mar 2026
The projections of a vector on the three coordinate axis are $6,-3,2$ respectively. The direction cosines of the vector are :
A.
${6 \over 5},{{ - 3} \over 5},{2 \over 5}$
B.
${6 \over 7 },{{ - 3} \over 7},{2 \over 7}$
C.
${- 6 \over 7 },{{ - 3} \over 7},{2 \over 7}$
D.
$6, -3, 2$
2008 Q367 JEE Mains MCQ
14 Mar 2026
The line passing through the points $(5,1,a)$ and $(3, b, 1)$ crosses the $yz$-plane at the point $\left( {0,{{17} \over 2}, - {{ - 13} \over 2}} \right)$ . Then
A.
$a=2,$ $b=8$
B.
$a=4,$ $b=6$
C.
$a=6,$ $b=4$
D.
$a=8,$ $b=2$
2008 Q368 JEE Mains MCQ
14 Mar 2026
If the straight lines $\,\,\,\,\,$ $\,\,\,\,\,$ ${{x - 1} \over k} = {{y - 2} \over 2} = {{z - 3} \over 3}$ $\,\,\,\,\,$ and$\,\,\,\,\,$ ${{x - 2} \over 3} = {{y - 3} \over k} = {{z - 1} \over 2}$ intersects at a point, then the integer $k$ is equal to
A.
$-5$
B.
$5$
C.
$2$
D.
$-2$
2007 Q369 JEE Mains MCQ
14 Mar 2026
If $(2,3,5)$ is one end of a diameter of the sphere ${x^2} + {y^2} + {z^2} - 6x - 12y - 2z + 20 = 0,$ then the coordinates of the other end of the diameter are
A.
$(4, 3, 5)$
B.
$(4, 3, -3)$
C.
$(4, 9, -3)$
D.
$(4, -3, 3)$
2007 Q370 JEE Mains MCQ
14 Mar 2026
Let $L$ be the line of intersection of the planes $2x+3y+z=1$ and $x+3y+2z=2.$ If $L$ makes an angle $\alpha $ with the positive $x$-axis, then cos $\alpha $ equals
A.
$1$
B.
${1 \over {\sqrt 2 }}$
C.
${1 \over {\sqrt 3 }}$
D.
${1 \over 2}$
2007 Q371 JEE Mains MCQ
14 Mar 2026
If a line makes an angle of $\pi /4$ with the positive directions of each of $x$-axis and $y$-axis, then the angle that the line makes with the positive direction of the $z$-axis is :
A.
${\pi \over 4}$
B.
${\pi \over 2}$
C.
${\pi \over 6}$
D.
${\pi \over 3}$
2006 Q372 JEE Mains MCQ
14 Mar 2026
The two lines $x=ay+b, z=cy+d;$ and $x=a'y+b' ,$ $z=c'y+d'$ are perpendicular to each other if :
A.
$aa'+cc'=-1$
B.
$aa'+cc'=1$
C.
${a \over {a'}} + {c \over {c'}} = - 1$
D.
${a \over {a'}} + {c \over {c'}} = 1$
2006 Q373 JEE Mains MCQ
14 Mar 2026
The image of the point $(-1, 3,4)$ in the plane $x-2y=0$ is :
A.
$\left( { - {{17} \over 3}, - {{19} \over 3},4} \right)$
B.
$(15,11,4)$
C.
$\left( { - {{17} \over 3}, - {{19} \over 3},1} \right)$
D.
None of these
2005 Q374 JEE Mains MCQ
14 Mar 2026
The plane $x+2y-z=4$ cuts the sphere ${x^2} + {y^2} + {z^2} - x + z - 2 = 0$ in a circle of radius
A.
$3$
B.
$1$
C.
$2$
D.
${\sqrt 2 }$
2005 Q375 JEE Mains MCQ
14 Mar 2026
The angle between the lines $2x=3y=-z$ and $6x=-y=-4z$ is :
A.
${0^ \circ }$
B.
${90^ \circ }$
C.
${45^ \circ }$
D.
${30^ \circ }$
2005 Q376 JEE Mains MCQ
14 Mar 2026
If the plane $2ax-3ay+4az+6=0$ passes through the midpoint of the line joining the centres of the spheres

${x^2} + {y^2} + {z^2} + 6x - 8y - 2z = 13$ and

${x^2} + {y^2} + {z^2} - 10x + 4y - 2z = 8$ then a equals :
A.
$-1$
B.
$1$
C.
$-2$
D.
$2$
2005 Q377 JEE Mains MCQ
14 Mar 2026
The distance between the line

$\overrightarrow r = 2\widehat i - 2\widehat j + 3\widehat k + \lambda \left( {i - j + 4k} \right),$ and the plane

$\overrightarrow r .\left( {\widehat i + 5\widehat j + \widehat k} \right) = 5$ is
A.
${{10} \over 9}$
B.
${{10} \over {3\sqrt 3 }}$
C.
${{3} \over 10}$
D.
${{10} \over 3}$
2005 Q378 JEE Mains MCQ
14 Mar 2026
If the angel $\theta $ between the line ${{x + 1} \over 1} = {{y - 1} \over 2} = {{z - 2} \over 2}$ and

the plane $2x - y + \sqrt \lambda \,\,z + 4 = 0$ is such that $\sin \,\,\theta = {1 \over 3}$ then value of $\lambda $ is :
A.
${5 \over 3}$
B.
${-3 \over 5}$
C.
${3 \over 4}$
D.
${-4 \over 3}$
2004 Q379 JEE Mains MCQ
14 Mar 2026
A line makes the same angle $\theta $, with each of the $x$ and $z$ axis.

If the angle $\beta \,$, which it makes with y-axis, is such that $\,{\sin ^2}\beta = 3{\sin ^2}\theta ,$ then ${\cos ^2}\theta $ equals :
A.
${2 \over 5}$
B.
${1 \over 5}$
C.
${3 \over 5}$
D.
${2 \over 3}$
2004 Q380 JEE Mains MCQ
14 Mar 2026
The intersection of the spheres
${x^2} + {y^2} + {z^2} + 7x - 2y - z = 13$ and
${x^2} + {y^2} + {z^2} - 3x + 3y + 4z = 8$
is the same as the intersection of one of the sphere and the plane
A.
$2x-y-z=1$
B.
$x-2y-z=1$
C.
$x-y-2z=1$
D.
$x-y-z=1$
2004 Q381 JEE Mains MCQ
14 Mar 2026
Distance between two parallel planes

$\,2x + y + 2z = 8$ and $4x + 2y + 4z + 5 = 0$ is :
A.
${9 \over 2}$
B.
${5 \over 2}$
C.
${7 \over 2}$
D.
${3 \over 2}$
2004 Q382 JEE Mains MCQ
14 Mar 2026
A line with direction cosines proportional to $2,1,2$ meets each of the lines $x=y+a=z$ and $x+a=2y=2z$ . The co-ordinates of each of the points of intersection are given by :
A.
$\left( {2a,3a,3a} \right),\left( {2a,a,a} \right)$
B.
$\left( {3a,2a,3a} \right),\left( {a,a,a} \right)$
C.
$\left( {3a,2a,3a} \right),\left( {a,a,2a} \right)$
D.
$\left( {3a,3a,3a} \right),\left( {a,a,a} \right)$
2004 Q383 JEE Mains MCQ
14 Mar 2026
If the straight lines
$x=1+s,y=-3$$ - \lambda s,$ $z = 1 + \lambda s$ and $x = {t \over 2},y = 1 + t,z = 2 - t,$ with parameters $s$ and $t$ respectively, are co-planar, then $\lambda $ equals :
A.
$0$
B.
$-1$
C.
$ - {1 \over 2}$
D.
$-2$
2003 Q384 JEE Mains MCQ
14 Mar 2026
The shortest distance from the plane $12x+4y+3z=327$ to the sphere

${x^2} + {y^2} + {z^2} + 4x - 2y - 6z = 155$ is
A.
$39$
B.
$26$
C.
$11{4 \over {13}}$
D.
$13$
2003 Q385 JEE Mains MCQ
14 Mar 2026
Two systems of rectangular axes have the same origin. If a plane cuts then at distances $a,b,c$ and $a', b', c'$ from the origin then
A.
${1 \over {{a^2}}} + {1 \over {{b^2}}} + {1 \over {{c^2}}} - {1 \over {a{'^2}}} - {1 \over {b{'^2}}} - {1 \over {c{'^2}}} = 0$
B.
$\,{1 \over {{a^2}}} + {1 \over {{b^2}}} + {1 \over {{c^2}}} + {1 \over {a{'^2}}} + {1 \over {b{'^2}}} + {1 \over {c{'^2}}} = 0$
C.
${1 \over {{a^2}}} + {1 \over {{b^2}}} - {1 \over {{c^2}}} + {1 \over {a{'^2}}} - {1 \over {b{'^2}}} - {1 \over {c{'^2}}} = 0$
D.
${1 \over {{a^2}}} - {1 \over {{b^2}}} - {1 \over {{c^2}}} + {1 \over {a{'^2}}} - {1 \over {b{'^2}}} - {1 \over {c{'^2}}} = 0$
2003 Q386 JEE Mains MCQ
14 Mar 2026
The radius of the circle in which the sphere

${x^2} + {y^2} + {z^2} + 2x - 2y - 4z - 19 = 0$ is cut by the plane

$x+2y+2z+7=0$ is
A.
$4$
B.
$1$
C.
$2$
D.
$3$
2003 Q387 JEE Mains MCQ
14 Mar 2026
The lines ${{x - 2} \over 1} = {{y - 3} \over 1} = {{z - 4} \over { - k}}$ and ${{x - 1} \over k} = {{y - 4} \over 2} = {{z - 5} \over 1}$ are coplanar if :
A.
$k=3$ or $-2$
B.
$k=0$ or $-1$
C.
$k=1$ or $-1$
D.
$k=0$ or $-3$
2003 Q388 JEE Mains MCQ
14 Mar 2026
The two lines $x=ay+b,z=cy+d$ and $x = a'y + b',z = c'y + d'$ will be perpendicular, if and only if :
A.
$aa' + cc' + 1 = 0$
B.
$aa' + bb'cc' + 1 = 0$
C.
$aa' + bb'cc' = 0$
D.
$\left( {a + a'} \right)\left( {b + b'} \right) + \left( {c + c'} \right) = 0$
2002 Q389 JEE Mains MCQ
14 Mar 2026
A plane which passes through the point $(3,2,0)$ and the line

${{x - 4} \over 1} = {{y - 7} \over 5} = {{z - 4} \over 4}$ is :
A.
$x-y+z=1$
B.
$x+y+z=5$
C.
$x+2y-z=1$
D.
$2x-y+z=5$
2002 Q390 JEE Mains MCQ
14 Mar 2026
The $d.r.$ of normal to the plane through $(1, 0, 0), (0, 1, 0)$ which makes an angle $\pi /4$ with plane $x+y=3$ are :
A.
$1,\sqrt 2 ,1$
B.
$1,1,\sqrt 2 $
C.
$1, 1, 2$
D.
$\sqrt 2 ,1,1$