R D Sharma Solutions for Chapter: Vector or Cross Product, Exercise 3: MULTIPLE CHOICE QUESTIONS (MCQs)

If $\overrightarrow{a}=\hat{i}+\hat{j}-\hat{k}, \overrightarrow{b}=-\hat{i}+2\hat{j}+2\hat{k}$ and $\overrightarrow{c}=-\hat{i}+2\hat{j}-\hat{k}$ then a unit vector normal to the vectors $\overrightarrow{a}+\overrightarrow{b}$ and $\overrightarrow{b}-\overrightarrow{c}$ is

A unit vector perpendicular to both $\hat{i}+\hat{j}$ and $\hat{j}+\hat{k}$ is

If $\overrightarrow{a}=2\hat{i}-3\hat{j}-\hat{k}$ and $\overrightarrow{b}=\hat{i}+4\hat{j}-2\hat{k}$, then $\overrightarrow{a}\times \overrightarrow{b}$ is 

If $\hat{i}, \hat{j}, \hat{k}$ are unit vectors, then

If $\theta$ is the angle between the vectors $2\hat{i}-2\hat{j}+4\hat{k}$ and $3\hat{i}+\hat{j}+2\hat{k}$  then $\sin \theta =$

If $|\overrightarrow{a}\times \overrightarrow{b}|=4,|\overrightarrow{a}·\overrightarrow{b}|=2$, then $\left|\overrightarrow{a}{|}^2\right|\overrightarrow{b}{|}^2=$

The value of $(\overrightarrow{a}\times \overrightarrow{b}{)}^2$ is

The value of $\hat{i}·(\hat{j}\times \hat{k})+\hat{j}·(\hat{i}\times \hat{k})+\hat{k}·(\hat{i}\times \hat{j})$ is