Question

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

Answer 1

Given, $a=\hat{i}+\hat{j}+2\hat{k}$ comparing with $x=a\hat{i}+b\hat{j}+ck,$ we get
a = 1, b = 1, c = 2
Magnitude of vector $a=|a|=\sqrt{a^2+b^2+c^2}=\sqrt{1^2+1^2+2^2}=\sqrt{6}$
$\therefore$ The unit vector $\hat{a}$ in the direction of vector $a=\hat{i}+\hat{j}+2\hat{k}$ is given by
$\hat{a}=\frac{a}{|a|}=\frac{1}{\sqrt{6}}(\hat{i}+\hat{j}+2\hat{k})=\frac{1}{\sqrt{6}}\hat{i}+\frac{1}{\sqrt{6}}\hat{j}+\frac{2}{\sqrt{6}}\hat{k}$