Question

Find unit vector in the direction of vector $\overrightarrow{a}=2\hat{i}+3\hat{j}+\hat{k}$

Answer 1

Given $\overrightarrow{a}-2\hat{i}+3\hat{j}+\hat{k}=2\hat{i}+3\hat{j}+1\hat{k}$

Magnitude of $\overrightarrow{a}-\sqrt{2^2+3^2+1^2}$

$\left|\overrightarrow{a}\right|=\sqrt{4+9+1}=\sqrt{14}.$

Unit vector in direction of $\overrightarrow{a}=\frac{1}{magnitudeof\overrightarrow{a}}\times \overrightarrow{a}$

$\overrightarrow{a}=\frac{1}{\sqrt{14}}[2\hat{i}+3\hat{j}+1\hat{k}]$

$\overrightarrow{a}=\frac{2}{\sqrt{14}}\hat{i}+\frac{3}{\sqrt{14}}\hat{j}+\frac{1}{\sqrt{14}}\hat{k}$

Thus, unit vector in direction of $\overrightarrow{a}$

$\frac{2}{\sqrt{14}}\hat{i}+\frac{3}{\sqrt{14}}\hat{j}+\frac{1}{\sqrt{14}}\hat{k}.$