Embibe Experts Solutions for Chapter: Mathematical Tools in Physics, Exercise 2: Exercise-2

If $\overrightarrow{\mathrm{a}}$ is a vector and $\mathrm{x}$ is a non-zero scalar, then

The two vectors $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$ are drawn from a common point and $\overrightarrow{\mathrm{C}}=\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}$ then angle between $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$ is

Which of the following expressions are meaningful?

The line of action of a force $\overrightarrow{\mathrm{F}}=\left(-3\hat{\mathrm{i}}+\hat{\mathrm{j}}+5\hat{\mathrm{k}}\right) \mathrm{N}$ passes through a point $(7,3,1)$. The moment of force $\left(\overrightarrow{\mathrm{\tau }}=\overrightarrow{\mathrm{r}}\times \overrightarrow{\mathrm{F}}\right)$ about the origin is given by

Position vector of a particle is given by $\overrightarrow{\mathrm{r}}=\mathrm{acos\omega t}\hat{\mathrm{i}}+\mathrm{asin\omega t}\hat{\mathrm{j}}$. Which of the following is/are true?

Force acting on a particle is $\left(2\hat{\mathrm{i}}+3\hat{\mathrm{j}}\right) \mathrm{N}.$ Work done by this force is zero, when the particle is moved on the line $3\mathrm{y}+\mathrm{Kx}=5.$ Here value of $\mathrm{K}$ is (work done $\overrightarrow{\mathrm{W}}=\overrightarrow{\mathrm{F}}·\overrightarrow{\mathrm{d}}$):

Equation of line $\mathrm{BA}$ is $\mathrm{x}+\mathrm{y}=1$. Find a unit vector along the reflected ray $\mathrm{AC}$.

The vector $(\overrightarrow{\mathrm{a}}+3\overrightarrow{\mathrm{b}})$ is perpendicular to $(7\overrightarrow{\mathrm{a}}-5\overrightarrow{\mathrm{b}})$ and $(\overrightarrow{\mathrm{a}}-4\overrightarrow{\mathrm{b}})$ is perpendicular to $(7\overrightarrow{\mathrm{a}}-2\overrightarrow{\mathrm{b}})$. The angle between $\overrightarrow{\mathrm{a}}$ and $\overrightarrow{\mathrm{b}}$ is :