List of all the Questions
Mark against the correct answer in each of the following:
If the plane $2 x-y+z=0$ is parallel to the line $\frac{2 x-1}{2}=\frac{2-y}{2}=\frac{z+1}{a}$, then the value of $a$ is
A. $-4$
B. $-2$
C. 4
D. 2
Mark against the correct answer in each of the following:
The equation of the plane passing through the points $A(0,-1,0), B(2,1,-1)$ and $C(1,1,1)$ is given by
A. $4 x+3 y-2 z-3=0$
B. $4 x-3 y+2 z+3=0$
C. $4 x-3 y+2 z-3=0$
D. None of these
Mark against the correct answer in each of the following:
The equation of the plane passing through the intersection of the planes $3 x-y+2 z-4=0$ and $x+y+z-2=0$ and passing through the point $A(2,2,1)$ is given by
A. $7 x+5 y-4 z-8=0$
B. $7 x-5 y+4 z-8=0$
C. $5 x-7 y+4 z-8=0$
D. $5 x+7 y-4 z+8=0$
Mark against the correct answer in each of the following:
The equation of the plane passing through the points $\mathrm{A}(2,2,1)$ and $\mathrm{B}(9,3,6)$ and perpendicular to the plane $2 x+6 y+6 z=1$, is
A. $x+2 y-3 z+5=0$
B. $2 x-3 y+4 z-6=0$
C. $4 x+5 y-6 z+3=0$
D. $3 x+4 y-5 z-9=0$
Mark against the correct answer in each of the following:
The line $\frac{x-1}{2}=\frac{y-2}{4}=\frac{z-3}{-3}$ meets the plane $2 x+3 y-z=14$ in the point
A. $(2,5,7)$
B. $(3,5,7)$
C. $(5,7,3)$
D. $(6,5,3)$
Mark against the correct answer in each of the following:
The equation of a plane through the point $A(1,0,-1)$ and perpendicular to the line $\frac{x+1}{2}=\frac{y+3}{4}=\frac{z+7}{-3}$ is
A. $2 x+4 y-3 z=3$
B. $2 x-4 y+3 z=5$
C. $2 x+4 y-3 z=5$
D. $x+3 y+7 z=-6$
Mark against the correct answer in each of the following:
If a plane meets the coordinate axes in $A, B$ and $C$ such that the centroid of $\triangle A B C$ is $(1,2,4)$, then the equation of the plane is
A. $x+2 y+4 z=6$
B. $4 x+2 y+z=12$
C. $x+2 y+4 z=7$
D. $4 x+2 y+z=7$
Mark against the correct answer in each of the following:
The plane $2 x+3 y+4 z=12$ meets the coordinate axes in $A, B$ and $C$. The centroid of $\triangle A B C$ is
A. $(2,3,4)$
B. $(6,4,3)$
C. $\left(2, \frac{4}{3}, 1\right)$
D. None of these
Mark against the correct answer in each of the following:
If the line $\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-k}{2}$ lies in the plane $2 x-4 y+z=7$, then the value of $k$ is
A. $-7$
B. 7
C. 4
D. $-4$
Mark against the correct answer in each of the following:
If $O$ is the origin and $P(1,2,-3)$ is a given point, then the equation of the plane through $P$ and perpendicular to OP is
A. $x+2 y-3 z=14$
B. $x-2 y+3 z=12$
C. $x-2 y-3 z=14$
D. None of these
Mark against the correct answer in each of the following:
If the line $\frac{x+1}{3}=\frac{y-2}{4}=\frac{z+6}{5}$ is parallel to the plane $2 x-3 y+k z=0$, then the value of $k$ is
A. $\frac{5}{6}$
B. $\frac{6}{5}$
C. $\frac{3}{4}$
D. $\frac{4}{5}$
Mark against the correct answer in each of the following:
A plane cuts off intercepts $3,-4,6$ on the coordinate axes. The length of perpendicular from the origin to this plane is
A. $\frac{5}{\sqrt{29}}$ units
B. $\frac{8}{\sqrt{29}}$ units
C. $\frac{6}{\sqrt{29}}$ units
D. $\frac{12}{\sqrt{29}}$ units
Mark against the correct answer in each of the following:
The equation of a plane passing through the point $A(2,-3,7)$ and making equal intercepts on the axes, is
A. $x+y+z=3$
B. $x+y+z=6$
C. $x+y+z=9$
D. $x+y+z=4$
Mark against the correct answer in each of the following:
The length of perpendicular from the origin to the plane $\overrightarrow{\mathrm{r}} \cdot(3 \hat{\mathrm{i}}-4 \hat{\mathrm{j}}-12 \hat{\mathrm{k}})+39=0$ is
A. 3 units
B. $\frac{13}{5}$ units
C. $\frac{5}{3}$ units
D. None of these
Mark against the correct answer in each of the following:
The direction cosines of the normal to the plane $5 y+4=0$ are
A. $0, \frac{-4}{5}, 0$
B. $0,1,0$
C. $0,-1,0$
D. None of these
Mark against the correct answer in each of the following:
The direction cosines of the perpendicular from the origin to the plane $\overrightarrow{\mathrm{r}} \cdot(6 \hat{\mathrm{i}}-3 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})+1=0$ are
A. $\frac{6}{7}, \frac{3}{7}, \frac{-2}{7}$
B. $\frac{6}{7}, \frac{-3}{7}, \frac{2}{7}$
C. $\frac{-6}{7}, \frac{3}{7}, \frac{2}{7}$
D. None of these
Write the equation of a plane passing through the point $(2,-1,1)$ and parallel to the plane $3 x+2 y-z=7$.
Write the angle between the line
$\frac{x-1}{2}=\frac{y-2}{1}=\frac{z+3}{-2}$ and the plane $x+y+4=0$
Find the value of $\lambda$ for which the line
$\frac{x-1}{2}=\frac{y-1}{3}=\frac{z-1}{2}$ is parallel to the plane $\bar{r} \cdot(2 \hat{\imath}+3 \hat{\jmath}+4 \hat{k})=4$
Find the length of perpendicular from the origin to the plane $\bar{r} \cdot(2 \hat{j}-3 \hat{j}+6 \hat{k})+14-0$.
