Embibe Experts Solutions for Chapter: Vector Algebra, Exercise 1: AMU-AT (B.Tech.) 2017

Let $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ be three vectors form $\overrightarrow{a}\times \left(\overrightarrow{b}\times \overrightarrow{c}\right)=\left(\overrightarrow{a}\times \overrightarrow{b}\right)\times \overrightarrow{c}$, if

If $\hat{\mathrm{i}},\hat{\mathrm{j}},\hat{\mathrm{k}}$ are unit vectors and ${\left|\overrightarrow{a}\right|}^2={\overrightarrow{a}}^2$, then the value of ${\left|\hat{\mathrm{i}}\times \overrightarrow{a}\right|}^2+{\left|\hat{\mathrm{j}}\times \overrightarrow{a}\right|}^2+{\left|\hat{\mathrm{k}}\times \overrightarrow{a}\right|}^2$ is

Let the unit vectors $a$ and $b$ be perpendicular to each other and the unit vector $c$ be inclined at an angle $\theta$ to both $a$ and $b$. If $c=\alpha a+\beta b+\gamma (a·b),$where $\alpha ,\beta ,\gamma$ are scalars, then

The unit vector which is orthogonal to the vector $\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}$ and is coplanar with vectors $\hat{\mathrm{i}}+2\hat{\mathrm{j}}-\hat{\mathrm{k}}$ and $2\hat{\mathrm{i}}+\hat{\mathrm{j}}+3\hat{\mathrm{k}},$ is

If the sum of two unit vectors is again a unit vector, then magnitude of their difference is