R D Sharma Solutions for Chapter: Scalar or Dot Product, Exercise 3: VERY SHORT ANSWER QUESTIONS (VSAQs)

Write the component of $\overrightarrow{b}$ along $\overrightarrow{a}$

Find the angle between the vectors $\overrightarrow{\mathrm{a}}=\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}}\text{ and }\overrightarrow{\mathrm{b}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}}$.

Find the projection of $\overrightarrow{\mathrm{a}}\text{ on }\overrightarrow{\mathrm{b}},\text{ if }\overrightarrow{\mathrm{a}}·\overrightarrow{\mathrm{b}}=8\text{ and }\overrightarrow{\mathrm{b}}=2\hat{\mathrm{i}}+6\hat{\mathrm{j}}+3\hat{\mathrm{k}}$

Write the value of $\mathrm{p}$ for which $\overrightarrow{\mathrm{a}}=3\hat{\mathrm{i}}+2\hat{\mathrm{j}}+9\hat{\mathrm{k}}\text{ and }\overrightarrow{\mathrm{b}}=\hat{\mathrm{i}}+\mathrm{p}\hat{\mathrm{j}}+3\hat{\mathrm{k}}$ are parallel vectors .

If $\left|\overrightarrow{\mathrm{a}}\right|=2,\text{ and }\overrightarrow{\mathrm{a}}·\overrightarrow{\mathrm{b}}=3$ find the projection of $\overrightarrow{\mathrm{b}}\text{ on }\overrightarrow{\mathrm{a}}$.

Write the angle between two vectors $\overrightarrow{\mathit{a}}$and $\overrightarrow{\mathrm{b}}$ with magnitudes$\sqrt{3}$ and$2$ respectively having $\overrightarrow{\mathrm{a}}·\overrightarrow{\mathrm{b}}=\sqrt{6}$

If the vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ are such that $\left|\overrightarrow{a}\right|=3, \left|\overrightarrow{b}\right|=\frac{2}{3}$ and $\overrightarrow{a}\times \overrightarrow{b}$ is a unit vector, then write the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$

Find the magnitude of each of the two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$, having the same magnitude such that the angle between them is $60°$ and their scalar product is $\frac{9}{2}$.