Umakant Kondapure, Collin Fernandes, Nipun Bhatia, Vikram Bathula and, Ketki Deshpande Solutions for Chapter: Scalars and Vectors, Exercise 3: Competitive Thinking

A particle moves from a point $\left(-2\hat{\mathrm{i}}+5\hat{\mathrm{j}}\right)$ to $\left(4\mathrm{j}+3\hat{\mathrm{k}}\right)$ when a force of $\left(4\hat{\mathrm{i}}+3\hat{\mathrm{j}}\right)\mathrm{N}$ is applied. How much work has been done by the force?

A force, $\overrightarrow{F}=-K\left(y\hat{\mathrm{i}}+x\hat{\mathrm{j}}\right)$ (where, $K$ is a positive constant) acts on a particle moving in the $x-y$ plane. Starting from the origin, the particle is taken along the positive $x$-axis to the point $\left(a,0\right)$ and then parallel to the $y$-axis to the point $\left(a,a\right)$. The total work done by the force $\overrightarrow{F}$ on the particle is,

The vector sum of two forces is perpendicular to their vector difference. In that case, the forces,

Which of the following statements is true?

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are two vectors, then the value of $\left(\overrightarrow{a}+\overrightarrow{b}\right)\times \left(\overrightarrow{a}-\overrightarrow{b}\right)$ is,

The angle between the vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ is $\theta$. The value of the triple product, $\overrightarrow{A}·(\overrightarrow{B}\times \overrightarrow{A})$ is,

The vectors $\overrightarrow{A}\text{,} \overrightarrow{B}$ and $\overrightarrow{C}$ are such that $\left|\overrightarrow{A}\right|=\left|\overrightarrow{B}\right|,\left|\overrightarrow{C}\right|=\sqrt{2}\left|\overrightarrow{A}\right|$ and $\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C}=0$. The angles between $\overrightarrow{A}$ and $\overrightarrow{B}\text{,} \overrightarrow{B}$ and $\overrightarrow{C}$, respectively, are,

The position of a particle is given by, $\overrightarrow{\mathit{r}}=3\mathrm{t}\hat{\mathrm{i}}-4{\mathrm{t}}^2\hat{\mathrm{j}}+5\hat{\mathrm{k}}.$ Then the magnitude of the velocity of the particle at $t=2 \mathrm{s}$ is