Umakant Kondapure, Collin Fernandes, Nipun Bhatia, Vikram Bathula and, Ketki Deshpande Solutions for Chapter: Scalars and Vectors, Exercise 1: Classical Thinking

If $\overrightarrow{P}=\hat{\mathrm{i}}+2\hat{\mathrm{j}}+\hat{\mathrm{k}}$ and $\overrightarrow{Q}=3\hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}}$ then $\overrightarrow{P}\times \overrightarrow{Q}$ is

Linear momentum $\overrightarrow{p}=2\hat{\mathrm{i}}+4\hat{\mathrm{j}}+5\hat{\mathrm{k}}$ and position vector is $\overrightarrow{r}=3\hat{\mathrm{i}}-\hat{\mathrm{j}}+2\hat{\mathrm{k}},$ the angular momentum is given by

The area of a triangle formed by the sides of vector $\overrightarrow{A}$ and $\overrightarrow{B}$ is

The area of the triangle having two sides $\overrightarrow{A}=\hat{\mathrm{i}}-2\hat{\mathrm{j}}-2\hat{\mathrm{k}}$ and $\overrightarrow{B}=2\hat{\mathrm{i}}+2\hat{\mathrm{j}}+3\hat{\mathrm{k}}$ is

Area of parallelogram whose adjacent sides are$\left(\hat{\mathrm{i}}+2\hat{\mathrm{j}}+3\hat{\mathrm{k}}\right)\mathrm{m}$ and $\left(\hat{\mathrm{i}}-3\hat{\mathrm{j}}+\hat{\mathrm{k}}\right)\mathrm{m}$ is

If $\overrightarrow{P}=\hat{\mathrm{i}}+2\hat{\mathrm{j}}-4\hat{\mathrm{k}}$ and $\overrightarrow{Q}=\hat{\mathrm{i}}+2\hat{\mathrm{j}}-\hat{\mathrm{k}}$, then $\left(\overrightarrow{P}+\overrightarrow{Q}\right)·\left(\overrightarrow{P}-\overrightarrow{Q}\right)$ is,

If $\overrightarrow{A}=2\hat{\mathrm{i}}+3\hat{\mathrm{j}}+4\hat{\mathrm{k}}$ and $\overrightarrow{B}=\hat{\mathrm{i}}+2\hat{\mathrm{j}}+3\hat{\mathrm{k}}$. The value of $\left(2\overrightarrow{A}-\overrightarrow{B}\right)·\left(\overrightarrow{A}+2\overrightarrow{B}\right)$ is,

A particle moves from position $\overrightarrow{s_1}=\left(3\hat{\mathrm{i}}+2\hat{\mathrm{j}}-6\hat{\mathrm{k}}\right)\mathrm{m}$ to position of $\overrightarrow{s_2}=\left(14\hat{\mathrm{i}}+13\hat{\mathrm{j}}+9\hat{\mathrm{k}}\right)\mathrm{m},$ under the action of a force$\overrightarrow{F}=\left(4\hat{\mathrm{i}}+\hat{\mathrm{j}}+3\hat{\mathrm{k}}\right)\mathrm{N}.$ The work done by the force is,