Embibe Experts Solutions for Chapter: Mathematical Methods, Exercise 1: Exercise 1

A particle is moving with speed $6 \mathrm{m} {\mathrm{s}}^{-1}$ along the direction of $\overrightarrow{A}=2\hat{\mathrm{i}}+2\hat{\mathrm{j}}-\hat{\mathrm{k}}$. Then its velocity 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 : 

The angle between two vectors $x$ and $y$ is $\theta$. If the resultant vector $z$ makes an angle $\frac{\theta }{2}$ with $x$, then which of the following is true?

If $\overrightarrow{A}$ and $\overrightarrow{B}$ are two non-zero vectors such that, $|\overrightarrow{A}+\overrightarrow{B}|=\frac{|\overrightarrow{A}-\overrightarrow{B}|}{2}$ and $\left|\overrightarrow{A}\right|=2\left|\overrightarrow{B}\right|$, then the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is 

Which of the following is a unit vector perpendicular to $\overrightarrow{A}$ and $\overrightarrow{B}$?

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are two vectors, then the value of $\left(\overrightarrow{a}+\overrightarrow{b}\right)\times \left(\overrightarrow{a}-\overrightarrow{b}\right)$ is,

Given, $\overrightarrow{A}=3\hat{\mathrm{i}}+2\hat{\mathrm{j}}$ and $\overrightarrow{B}=\hat{\mathrm{i}}+\hat{\mathrm{j}}$. The component of vector $\overrightarrow{A}$ along vector $\overrightarrow{B}$ is

The angle between two vectors of equal magnitudes whose resultant is equal to the magnitude of the either vector is