Embibe Experts Solutions for Chapter: Mathematical Tools in Physics, Exercise 16: Exercise (Assertion & Reason)

A vector $\overrightarrow{A}$ points vertically upward and $\overrightarrow{B}$ points towards north. The vector product $\overrightarrow{A}\times \overrightarrow{B}$ is

If $\left|\overrightarrow{\mathrm{A}}\times \overrightarrow{\mathrm{B}}\right|=\left|\overrightarrow{\mathrm{A}}·\overrightarrow{\mathrm{B}}\right|$, then angle between $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$ will be

Three vectors satisfy the relation, $\overrightarrow{A}·\overrightarrow{B}=0$ and $\overrightarrow{A}·\overrightarrow{C}=0$. Then, $\overrightarrow{A}$ is parallel to,

The vectors $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$ are such that $\left|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}\right|=\left|\overrightarrow{\mathrm{A}}-\overrightarrow{\mathrm{B}}\right|$.

The angle between vectors $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$ is:

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

Find the torque of a force $\overrightarrow{F}=-3\hat{i}+\hat{j}+5\hat{k}$ acting at a point $\overrightarrow{r}=7\hat{i}+3\hat{j}+\hat{k}$

If vectors $\overrightarrow{A}=\cos \left(\omega t\right)\hat{\mathrm{i}}+\sin \left(\omega t\right)\hat{\mathrm{j}}$ and $\overrightarrow{B}=\cos \left(\frac{\omega t}{2}\right)\hat{\mathrm{i}}+\sin \left(\frac{\omega t}{2}\right)\hat{\mathrm{j}}$ are functions of time then the value of $t$ at which they are orthogonal to each other is,

If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is,