Embibe Experts Solutions for Chapter: Vector Algebra, Exercise 1: SRMJEEE (UG) 2014

The non-zero vectors $\overrightarrow{a},\overrightarrow{b}$ and $\overrightarrow{c}$ are related by $\overrightarrow{a}=8\overrightarrow{b},\overrightarrow{c}=-7\overrightarrow{b}.$ Then the angle between $\overrightarrow{a}$ and $\overrightarrow{c}$ is

Let $\overrightarrow{u}=\hat{i}+\hat{j},\overrightarrow{v}=\hat{i}-\hat{j},\overrightarrow{w}=\hat{i}+2\hat{j}+3\hat{k}.$ If $\hat{n}$ is a unit vector such that $\overrightarrow{u}·\hat{n}=0,\overrightarrow{v}·\hat{n}=0$. Then $|\overrightarrow{w}·\hat{n}|=$

If $\overrightarrow{A}=4\hat{i}+3\hat{j}+\hat{k},\overrightarrow{B}=2\hat{i}+\hat{j}+2\hat{k},$ the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is given by

A unit vector perpendicular to $-\hat{i}+2\hat{j}+2\hat{k}$ and making equal angles with $x$ and $y$ axes $canb$

If $\overrightarrow{a}=\hat{i}+\hat{j}+\hat{k},\overrightarrow{b}=\hat{i}-\hat{j}+\hat{k},\overrightarrow{c}=\hat{i}+2\hat{j}-\hat{k}$
then $\left|\begin{array}{lll}\overrightarrow{a}·\overrightarrow{a}& \overline{a}·\overrightarrow{b}& \overrightarrow{a}·\overrightarrow{c}\\ \overrightarrow{b}·\overrightarrow{a}& \overrightarrow{b}·\overrightarrow{b}& \overrightarrow{b}·\overline{c}\\ \overrightarrow{c}·\overrightarrow{a}& \overrightarrow{c}·\overrightarrow{b}& \overrightarrow{c}·\overrightarrow{c}\end{array}\right|=$

If $\left|\overrightarrow{a}\right|=2,\left|\overrightarrow{b}\right|=3,\left|\overrightarrow{c}\right|=4$ and $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0},$ then the value of $\overrightarrow{b}·\overrightarrow{c}+\overrightarrow{c}·\overrightarrow{a}+\overrightarrow{a}·\overrightarrow{b}$ is equal to