Embibe Experts Solutions for Chapter: Mathematical Tools in Physics, Exercise 3: Exercise-3

The motion of a particle along a straight line is described by the equation : $x=8+12t-t^3$, where $x$ is in metre and $t$ is in second. The retardation of the particle when its velocity becomes zero, is

The vectors $\overrightarrow{A}$ and $\overline{B}$ are such that : $\left|\overrightarrow{A}+\overrightarrow{B}\right|=\left|\overrightarrow{A}-\overrightarrow{B}\right|$ The angle between the two vectors is:

Six vectors, $\overrightarrow{a}$ through $\overrightarrow{f}$ have the mangitudes and directions indicated in the figure. Which of the following statements is true?

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

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

In the cube of side $\text{'}a\text{'}$ shown in the figure, the vector from the central point of the face $ABOD$ to the central point of the face $BEFO$ will be : 

Two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ have equal magnitudes. The magnitude of $\left(\overrightarrow{A}+\overrightarrow{B}\right)$ is $n$ times the magnitude of $\left(\overrightarrow{A}-\overrightarrow{B}\right)$ . The angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is: