Embibe Experts Solutions for Exercise 4: EXERCISE 11.4

If $\overrightarrow{A}=2\hat{i}+\hat{k}, \overrightarrow{B}=\hat{i}+\hat{j}+\hat{k}$ and $\overrightarrow{C}=4\hat{i}-3\hat{j}+7\hat{k},$ then a vector $\overrightarrow{r}$ which satisfies $\overrightarrow{r}\times \overrightarrow{B}=\overrightarrow{C}\times \overrightarrow{B}$ and $\overrightarrow{r}·\overrightarrow{A}=0,$ is

If $\overrightarrow{x}\times \overrightarrow{b}=\overrightarrow{c}\times \overrightarrow{b}$ and $\overrightarrow{x}\perp \overrightarrow{a},$ then $\overrightarrow{x}$ is equal to

If $\overrightarrow{a}$ is a unit vector, $\overrightarrow{a}\times \overrightarrow{r}=\overrightarrow{b}, \overrightarrow{a}·\overrightarrow{r}=c, \overrightarrow{a}·\overrightarrow{b}=0$, then $\overrightarrow{r}$ is

If $\overrightarrow{x}+\overrightarrow{y}=\overrightarrow{a}, \overrightarrow{x}\times \overrightarrow{y}=\overrightarrow{b}$ and $\overrightarrow{x}·\overrightarrow{a}=1,$ then

A unit vector in $XY$-plane that makes an angle $45°$ with the vector $\hat{i}+\hat{j}$ and angle $60°$ with $3\hat{i}-4\hat{j}$ is

If $\overrightarrow{a}·\overrightarrow{b}=\beta$ and $\overrightarrow{a}\times \overrightarrow{b}=\overrightarrow{c},$, then $\overrightarrow{b}$ is equal to

Let the unit vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ be perpendicular to each other and the unit vector $\overrightarrow{c}$ be inclined at an angle $\theta$ to both $\overrightarrow{a}$ and $\overrightarrow{b}$. If $\overrightarrow{c}=x\overrightarrow{a}+y\overrightarrow{b}+z\left(\overrightarrow{a}\times \overrightarrow{b}\right)$, then

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