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

If $\overrightarrow{a}+3\overrightarrow{b} \text{and} 4\overrightarrow{a}+m\overrightarrow{b}$ are parallel, then the value of $m$ is

The three vectors $7\hat{i}-11\hat{j}+\hat{k}$, $5\hat{i}+3\hat{j}-2\hat{k}$ and $12\hat{i}-8\hat{j}-\hat{k}$

Two forces are such that the sum of their magnitudes is $18N$ and the magnitude of their resultant is $12N$. If the resultant is perpendicular to the smaller forces, then the magnitudes of the forces are –

$(\hat{i}+\hat{k})\times (\hat{i}+\hat{j}+\hat{k})=$

A vector perpendicular to the vectors $\hat{i}+\hat{j}$ and $\hat{i}+\hat{k}$ is

If $\hat{a}$ and $\hat{b}$ are unit vectors such that $\hat{a}\times \hat{b}$ is a unit vector, then the angle between $\hat{a}$ and $\hat{b}$ is 

If $\overrightarrow{a},\overrightarrow{b},$ and $\overrightarrow{c}$ are non-zero distinct vectors, then $\overrightarrow{a}\times \overrightarrow{b}=\overrightarrow{a}\times \overrightarrow{c}\iff$

The area of the triangle with vertices $(1,0,0),(0,1,0),$ and $(0,0,1)$ is