R S Aggarwal Solutions for Exercise 1: EXERCISE

If the magnitude of the vector $\overrightarrow{a}=\hat{i}+2\hat{j}+5\hat{k}$ is $\sqrt{m}$, where $m$ is a positive integer. Then $m$ is

If the magnitude of the vector $\overrightarrow{b}=5\hat{i}-4\hat{j}-3\hat{k}$ is $k\sqrt{2}$, then find the value of $k$.

The magnitude of $\overrightarrow{c}=\left(\frac{1}{\sqrt{3}}\hat{\mathit{i}}-\frac{1}{\sqrt{3}}\hat{j}+\frac{1}{\sqrt{3}}\hat{\mathit{k}}\right)$ is 

Write down the square of the magnitude of vector: $\overrightarrow{d}=(\sqrt{2}\hat{i}+\sqrt{3}\hat{j}-\sqrt{5}\hat{k})$

If $\overrightarrow{a}=(2\hat{i}-4\hat{j}+5\hat{k})$, then find the value of $\lambda$, so that $\lambda \overrightarrow{\mathit{a}}$, may be a unit vector.

Find the position vector of the point which divides the join of the points $(2\overrightarrow{a}-3\overrightarrow{b})$ and $(3\overrightarrow{a}-2\overrightarrow{b})$ externally in the ratio $2:3$.

Find the position vector of a point $R$ which divides the line joining $A(-2,1,3)$ and $B(3,5,-2)$ in the ratio $2:1$ externally.

If $\overrightarrow{AB}=(2\hat{i}+\hat{j}-3\hat{k})$ and $A(1,2,-1)$ is the given point, find the coordinates of $B$.