Let $\overrightarrow {\bf{a}} = \hat i + 2\hat j + 3\hat k,\overrightarrow {\bf{b}} = 3\hat i + \hat j - \hat k$ and $\vec c$...

Let the line passing through the points (-1, 2, 1) and parallel to the line $\frac{{x - 1}}{2} = \frac{{y + 1}}{3} = \frac{z}{4}$ intersect...

Let P be the foot of the perpendicular from the point $Q(10, - 3, - 1)$ on the line $...

Let the position vectors of the vertices A, B and C of a tetrahedron A, B, C, D be $...

Let the arc AC of a circle subtend a right angle at the centre O . If the point B on the $\operatorname{arc}\text{AC}$, divides the...

The perpendicular distance, of the line $\frac{x-1}{2}=\frac{y+2}{-1}=\frac{z+3}{2}$ from the point $\mathrm{P}(2,-10,1)$, is :

Let $\mathrm{L}_1: \frac{x-1}{3}=\frac{y-1}{-1}=\frac{z+1}{0}$ and $\mathrm{L}_2: \frac{x-2}{2}=\frac{y}{0}=\frac{z+4}{\alpha}, \alpha \in \mathbf{R}$, be two lines, which intersect at the point $B$. If $P$ is the foot of perpendicular...

Let $\vec{c}$ be the projection vector of $\vec{b}=\lambda \hat{i}+4 \hat{k}, \lambda>0$, on the vector $\vec{a}=\hat{i}+2 \hat{j}+2 \hat{k}$. If $|\vec{a}+\vec{c}|=7$, then the area of the parallelogram...

Let $\vec{a}$ and $\vec{b}$ be two unit vectors such that the angle between them is $\frac{\pi}{3}$. If $\lambda \vec{a}+2 \vec{b}$ and $3 \vec{a}-\lambda \vec{b}$ are...