Embibe Experts Solutions for Chapter: Vector Algebra, Exercise 2: EXERCISE-2

If two pairs of opposite edges of a tetrahedron are perpendicular then-

A non-zero vector $\overrightarrow{a}$ is parallel to the line of intersection of the plane determined by the vectors $\hat{i}, \hat{i}+\hat{j}$ and the plane determined by the vectors $\hat{i}-\hat{j}, \hat{i}+\hat{k}$. The possible angle between $\overrightarrow{a}$ and $\widehat{i}-2\widehat{j}+2\widehat{k}$ is-

If the non zero vectors $\overrightarrow{a}$ & $\overrightarrow{b}$ are perpendicular to each other then the solution of the equation $\overrightarrow{r}\times \overrightarrow{a}=\overrightarrow{b}$ is

If $\left(\overrightarrow{a}\times \overrightarrow{b}\right)\times \overrightarrow{c}=\overrightarrow{a}\times \left(\overrightarrow{b}\times \overrightarrow{c}\right)$, where $\overrightarrow{a}, \overrightarrow{b}$ and $\overrightarrow{c}$ are any three vectors such that $\overrightarrow{a}·\overrightarrow{b}\ne 0, \overrightarrow{b}·\overrightarrow{c}\ne 0$ then $\overrightarrow{a}$ and $\overrightarrow{c}$ are

If $\overrightarrow{a}, \overrightarrow{b} \& \overrightarrow{c}$ are non-coplanar unit vectors such that $\overrightarrow{a}\times \left(\overrightarrow{b}\times \overrightarrow{c}\right)=\frac{\overrightarrow{b}+\overrightarrow{c}}{\sqrt{2}}$, then the angle between

If $\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}, \overrightarrow{d}, \overrightarrow{e}, \overrightarrow{f}$ are position vectors of $6$ points $A, B, C, D, E$ and $F$ respectively such that $3\overrightarrow{a}+4\overrightarrow{b}=6\overrightarrow{c}+\overrightarrow{d}=4\overrightarrow{e}+3\overrightarrow{f}=\overrightarrow{x}$, then

The vector $\frac{1}{3}\left(2\hat{i}-2\hat{j}+\hat{k}\right)$ is-

If a vector $\overrightarrow{r}$ of magnitude $3\sqrt{6}$ is collinear with the bisector of the angle between the vector $\overrightarrow{a}=7\hat{i}-4\hat{j}-4\hat{k}$ and $\overrightarrow{b}=-2\hat{i}-\hat{j}+2\hat{k}$, then $\overrightarrow{r}=$