Embibe Experts Solutions for Chapter: Mathematical Tools in Physics, Exercise 1: Exercise-1

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

The projection of $\overrightarrow{A}$ on $\overrightarrow{B}$ is

Given that $\mathrm{P}=\mathrm{Q}=\mathrm{R}$. If $\overrightarrow{\mathrm{P}}+\overrightarrow{\mathrm{Q}}=\overrightarrow{\mathrm{R}}$ then the angle between $\overrightarrow{\mathrm{P}}$ and $\overrightarrow{\mathrm{R}}$ is ${\mathrm{\theta }}_1$. If $\overrightarrow{\mathrm{P}}+\overrightarrow{\mathrm{Q}}+\overrightarrow{\mathrm{R}}=\overrightarrow{0}$ then the angle between $\overrightarrow{\mathrm{P}}$ and $\overrightarrow{\mathrm{R}}$is ${\mathrm{\theta }}_2$.The relation between ${\mathrm{\theta }}_1$ and ${\mathrm{\theta }}_2$ is :-

Two balls are rolling on a flat smooth table. One ball has velocity components $\sqrt{3} \hat{\mathrm{j}}$ and $\hat{\mathrm{i}}$ while the other has components $2\hat{\mathrm{i}}$ and $2\hat{\mathrm{j}}$. If both start moving simultaneously from the same point, the angle between their paths is -

Select incorrect statement

Three concurrent forces of the same magnitude are in equilibrium. What is the angle between the forces? Also name the triangle formed by the forces as sides

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

A man is crossing a river flowing with velocity of $5 {\mathrm{ms}}^{-1}$. He reaches a point directly across at distance of $60 \mathrm{m}$ in $5\mathrm{s}$. His velocity in still water should be: