Embibe Experts Solutions for Chapter: Vectors, Exercise 1: Exercise 1

If $\overrightarrow{a}=\hat{i}+\hat{j},\overrightarrow{b}=\hat{j}+\hat{k},\overrightarrow{c}=\hat{k}+\hat{i},$ a unit vector parallel to $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}.$

If $OACB$ is a parallelogram with $\overrightarrow{OC}=\overrightarrow{a}$ and $\overrightarrow{AB}=\overrightarrow{b,}$ then $\overrightarrow{OA}$ is equal to

Given two vectors
$\overrightarrow{a}=2\hat{i}-3\hat{j}+6\hat{k},\overrightarrow{b}=-2\hat{i}+2\hat{j}-\hat{k}$ and
$\lambda =\frac{ \mathrm{the} \mathrm{projection} \mathrm{of} \overrightarrow{a} \mathrm{on} \overrightarrow{b}}{ \mathrm{the} \mathrm{projection} \mathrm{of} \overrightarrow{b} \mathrm{on} \overrightarrow{a}}$, then the value of $\lambda$
is

The area of parallelogram whose diagonals coincide with the following pair of vectors is $5\sqrt{3}.$ The vectors are

If $\overrightarrow{a}$ is any vector, then $(\overrightarrow{a}\times \hat{i}{)}^2+(\overrightarrow{a}\times \hat{j}{)}^2+(\overrightarrow{a}\times \hat{k}{)}^2$ is equal to

The vectors $2\hat{i}-m\hat{j}+3m\hat{k}$ and $(1+m)\hat{i}-2m\hat{j}+\hat{k}$ include an acute angle for

If $\left[\right(2\overrightarrow{a}+\overrightarrow{b}\left)\overrightarrow{c}\overrightarrow{d}\right]=\lambda \left[\overrightarrow{a}\overrightarrow{c}\overrightarrow{d}\right]+\mu \left[\overrightarrow{b}\overrightarrow{c}\overrightarrow{d}\right]$ then $\lambda +\mu$ is equal to

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are three non-coplanar vectors such that $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\alpha \overrightarrow{d}$ and $\overrightarrow{b}+\overrightarrow{c}+\overrightarrow{d}=\beta \overrightarrow{a}$ then $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}+\overrightarrow{d}$ is equal to