Embibe Experts Solutions for Chapter: Vector Algebra, Exercise 1: KEAM 2019

If the points with position vectors $30\hat{i}+3\hat{j}, 20\hat{i}+6\hat{j}$ and $5\hat{i}+b\hat{j}$ are collinear, then $b$ equal

If $\left|\overrightarrow{a}\right|=\left|\overrightarrow{b}\right|=|\overrightarrow{a}-\overrightarrow{b}|=1.$ Then angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are unit vectors and $\theta$ is the angle between them, then $\left|\frac{\overrightarrow{a}-\overrightarrow{b}}{2}\right|$ is

The projections of a line on the axes are $3, 4 , 5.$  The length of the line is

If $a·\hat{i}=a·(\hat{i}+\hat{j})=a·(\hat{i}+\hat{j}+\hat{k}),$ then $a$ is equal to

If $\theta$ is the angle between the vectors $4(\hat{i}-\hat{k})$ and $(\hat{i}+\hat{j}+\hat{k}),$ then the value of $(\sin \theta +\cos \theta )$ equal to

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are unit vectors, then the greatest value of $|\overrightarrow{a}+\overrightarrow{b}|+|\overrightarrow{a}-\overrightarrow{b}|$ is

The value of $[a-b,b-c,c-a]$ is equal to