Embibe Experts Solutions for Chapter: Mathematical Tools in Physics, Exercise 1: Exercise 1

Determine that vector which when added to the resultant of $\overrightarrow{P}=2\hat{\mathrm{i}}+7\hat{\mathrm{i}}-10\hat{\mathrm{k}}$ and $\overrightarrow{Q}=\hat{\mathrm{i}}+2\hat{\mathrm{j}}+3\hat{\mathrm{k}}$ gives a unit vector along X-axis.

Six vectors, $\overrightarrow{a}$ through $\overrightarrow{f}$ have the mangitudes and directions indicated in the figure. Which of the following statements is true?

In the figure, $\overrightarrow{E}$ equals

In figure, $\overrightarrow{D}-\overrightarrow{C}$ equals

Let $\overrightarrow{a}$ and $\overrightarrow{b}$ be two non-null vectors such that $\left|\overrightarrow{a}+\overrightarrow{b}\right|=\left|\overrightarrow{a}-2\overrightarrow{b}\right|.$ Then the value of $\frac{\left|\overrightarrow{a}\right|}{\left|\overrightarrow{b}\right|}$ may be:

If $\left|\overrightarrow{A}\right|=4, \left|\overrightarrow{B}\right|=3$ and $\theta =60°$ in the figure, Find $\left(a\right) \overrightarrow{A}·\overrightarrow{B}, \left(b\right) \left|\overrightarrow{A}\times \overrightarrow{B}\right|$

If $\overrightarrow{A}=4\hat{\mathrm{i}}+n\hat{\mathrm{j}}-2\hat{\mathrm{k}}$ and $\overrightarrow{B}=2\hat{\mathrm{i}}+3\hat{\mathrm{j}}+\hat{\mathrm{k}},$ then find the value of $n$ so that $\overrightarrow{A}\perp \overrightarrow{B}.$

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