Umakant Kondapure, Collin Fernandes, Nipun Bhatia, Vikram Bathula and, Ketki Deshpande Solutions for Chapter: Scalars and Vectors, Exercise 4: Evaluation Test

A particle acted upon by constant forces $5\hat{\mathrm{i}}+\hat{\mathrm{j}}-2\hat{\mathrm{k}}$ and $2\hat{\mathrm{i}}+\hat{\mathrm{j}}-2\hat{\mathrm{k}}$ is displaced from the point $2\hat{\mathrm{i}}+2\hat{\mathrm{j}}-4\hat{\mathrm{k}}$ to point $6\hat{\mathrm{i}}+4\hat{\mathrm{j}}-2\hat{\mathrm{k}}$. The total work done by the forces in SI unit is

The $x$ and $y$ components of vector $\overrightarrow{\mathrm{A}}$ are $4 \mathrm{m}$ and $6 \mathrm{m}$ respectively. The $\mathrm{x}$ and $\mathrm{y}$ components of vector $(\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}})$ are $12 \mathrm{m}$ and $10 \mathrm{m}$
respectively. Then what are the $x$ and $y$ components of vector $\overrightarrow{\mathrm{B}}?$

The angle subtended by the vector $A=6\hat{\mathrm{i}}+3\hat{\mathrm{j}}+4\hat{\mathrm{k}}$ with the $y$-axis is

A particle moves in the $x$-$y$ plane under the action of a force $\overrightarrow{F}$ such that the components of its linear momentum $\overrightarrow{p}$ at any time $t$ are $p_{\mathrm{x}}=3\cos t$ and $p_{\mathrm{y}}=3\sin t$. What is the magnitude of the vector $\overrightarrow{F}$?

Given, $\overrightarrow{A}=3\hat{\mathrm{i}}+2\hat{\mathrm{j}}$ and $\overrightarrow{B}=\hat{\mathrm{i}}+\hat{\mathrm{j}}$. The component of vector $\overrightarrow{A}$ along vector $\overrightarrow{B}$ is

A vector $\overrightarrow{A}$ is along the positive $x$-axis and its vector product with another vector $\overrightarrow{B}$ is zero. Then, vector $\overrightarrow{B}$ could be,

What is the area of the triangle formed by sides $\overrightarrow{A}=2\hat{\mathrm{i}}-3\hat{\mathrm{j}}+4\hat{\mathrm{k}}$ and  $\overrightarrow{B}=\hat{\mathrm{i}}-2\hat{\mathrm{k}}?$

The component of vector $\overrightarrow{A}=a_x\hat{\mathrm{i}}+{\mathrm{a}}_{\mathrm{y}}\hat{\mathrm{j}}+{\mathrm{a}}_{\mathrm{z}}\hat{\mathrm{k}}$ along the direction of $\hat{\mathrm{j}}-\hat{\mathrm{k}}$ is