R S Aggarwal Solutions for Exercise 4: OBJECTIVE QUESTIONS

If $\overrightarrow{a},\overrightarrow{b}$ and $\overrightarrow{c}$are mutually perpendicular unit vectors then $|\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}|=?$

$\left[\begin{array}{lll}\hat{i}& \hat{j}& \hat{k}\end{array}\right]=$

If $\overrightarrow{a}=(2\hat{i}-3\hat{j}+4\hat{k}), \overrightarrow{b}=(\hat{i}+2\hat{j}-\hat{k})$ and $\overrightarrow{c}=(3\hat{i}-\hat{j}-2\hat{k})$ be the coterminous edges of a parallelepiped then its volume is

If the volume of a parallelepiped having $\overrightarrow{a}=(5\hat{i}-4\hat{j}+\hat{k})$,$\overrightarrow{b}=(4\hat{i}+3\hat{j}+\lambda \hat{k})$ and $\overrightarrow{c}=(\hat{i}-2\hat{j}+7\hat{k})$ as coterminous edges, is $216$cubic units then the value of $\lambda$ is

It is given that the vectors $\overrightarrow{a}=(2\hat{i}-2\hat{k}), \overrightarrow{b}=\hat{i}+(\lambda +1)\hat{j}$ and $\overrightarrow{c}=(4 \hat{i}+2 \hat{k})$ are coplanar. Then, the value of $\lambda$ is

Which of the following is meaningless?

$\overrightarrow{a}·(\overrightarrow{a}\times \overrightarrow{b})=$

 For any three vectors $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ the value of $\left[\begin{array}{lll}\overrightarrow{a}-\overrightarrow{b}& \overrightarrow{b}-\overrightarrow{c}& \overrightarrow{c}-\overrightarrow{a}\end{array}\right]$ is