BM Sharma Solutions for Chapter: Vectors, Exercise 5: DPP

The angle between vectors $\left(\overrightarrow{\mathit{A}}\mathit{\times }\overrightarrow{\mathit{B}}\right)$ and $\left(\overrightarrow{B}\times \overrightarrow{A}\right)$ is

 If  $\overrightarrow{\mathit{A}}$ points vertically upward and $\overrightarrow{\mathit{B}}$ points towards north, then the vector product $\overrightarrow{\mathit{A}}\mathit{\times }\overrightarrow{\mathit{B}}$ is

Two vectors  $\overrightarrow{\mathit{A}}$ and $\overrightarrow{\mathit{B}}$ have equal magnitudes. The vector $\overrightarrow{\mathit{A}}\mathit{+}\overrightarrow{\mathit{B}}$ is perpendicular to

The value of $\left(\overrightarrow{\mathit{A}}\mathit{+}\overrightarrow{\mathit{B}}\right)\mathit{ }\mathit{\times }\mathit{ }\mathit{(}\overrightarrow{\mathit{A}}\mathit{-}\overrightarrow{\mathit{B}}\mathit{)}$  is

The linear velocity of a rotating body is given by $\overrightarrow{v}=\overrightarrow{\omega }\times \overrightarrow{r}$, where $\overrightarrow{\omega }$ is the angular velocity and $\overrightarrow{r}$is the radius vector. If the angular velocity of a body is $\overrightarrow{\omega }=\hat{\mathrm{i}}-2\hat{\mathrm{j}}+2\hat{\mathrm{k}}$ and the radius vector is $\overrightarrow{r}=4\hat{\mathrm{j}}-3\hat{\mathrm{k}}$, then $\left|\overrightarrow{v}\right|$ is 

Two adjacent sides of a parallelogram are represented by the two vectors $\hat{\mathrm{i}}+2\hat{\mathrm{j}}+3\hat{\mathrm{k}}$ and $3\hat{\mathrm{i}}-2\hat{\mathrm{j}}+\hat{\mathrm{k}}$. What is the area of the parallelogram?

The vectors from origin to the points $\mathrm{A}$ and $\mathrm{B}$  are $\overrightarrow{\mathit{A}}=3\hat{\mathrm{i}}-6\hat{\mathrm{j}}+2\hat{\mathrm{k}}$ and $\overrightarrow{\mathit{B}}=2\hat{\mathrm{i}}+\hat{\mathrm{j}}-2\hat{\mathrm{k}}$, respectively. The area of the$△\mathrm{OAB}$ is 

If  $\left|\overrightarrow{A}\times \overrightarrow{B}\right|=\sqrt{3} \overrightarrow{A}\bullet \overrightarrow{B}$, then find the value of $\left|\overrightarrow{A}+\overrightarrow{B}\right|$.