Algebra of Vectors — Maths STD 12 Science — Question

Then, $\big|\vec{\text{a}}\big|=\sqrt{3^2+4^2+(-12)^2}$

$=\sqrt{9+16+144}$

$=\sqrt{169}$

$=13$

So, a unit vector in the direction of $\vec{\text{a}}$ is given by

$\hat{\text{a}}=\frac{\vec{\text{a}}}{|\vec{\text{a}}|}=\frac{1}{13}\big(3\hat{\text{i}}+4\hat{\text{j}}-12\hat{\text{k}}\big)$

$=\frac{3}{13}\hat{\text{i}}+\frac{4}{13}\hat{\text{j}}-\frac{12}{13}\hat{\text{k}}$