A plane which bisects the angle between the two given planes 2x – y + 2z – 4 = 0 and x + 2y +...

A plane passing through the point $(3,1,1)$ contains two lines whose direction ratios are $1,-2,2$ and $2,3,-1$ respectively. If this plane also passes through the...

Let $\vec{a}, \vec{b}$ and $\vec{c}$ be three unit vectors such that $|\vec{a}-\vec{b}|^2+|\vec{a}-\vec{c}|^2=8$. Then $|\vec{a}+2 \vec{b}|^2+|\vec{a}+2 \vec{c}|^2$ is equal to

The plane passing through the points (1, 2, 1), (2, 1, 2) and parallel to the line, 2x = 3y, z = 1 also passes...

The sum of the distinct real values of $\mu$, for which the vectors, $\mu \hat{j}+\hat{j}+\hat{k}, \hat{i}+\mu \hat{j}+\hat{k}, \hat{i}+\hat{j}+\mu \hat{k}$ are co-planar, is

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 $O P Q$ and $P Q R$ is

The perpendicular distance from the origin to the plane containing the two lines,
$\frac{x+2}{3}=\frac{y-2}{5}=\frac{z+5}{7}$ and $\frac{x-1}{1}=\frac{y-4}{4}=\frac{z+4}{7}$ is

The equation of the plane containing the straight line $\frac{x}{2}=\frac{y}{3}=\frac{z}{4}$ and perpendicular to the plane containing the straight lines $\frac{x}{3}=\frac{y}{4}=\frac{z}{2}$ and $\frac{x}{4}=\frac{y}{2}=\frac{z}{3}$ is

If the vectors, $\vec{p}=(a+1) \hat{i}+a \hat{j}+a \hat{k}$, $\overrightarrow{\mathrm{q}}=\mathrm{a} \hat{\mathrm{i}}+(\mathrm{a}+1) \hat{\mathrm{j}}+\mathrm{a} \hat{\mathrm{k}}$, and $\vec{r}=a \hat{i}+a \hat{j}+(a+1) \hat{k}(a \in R)$ are coplanar and $...

The projection of the line segment joining the point (1, –1, 3) and (2, –4, 11) on the line joining the points (–1, 2, 3)...