Write the unit vector in the direction of a =3 i +2 j +6 k . - Vidyadip

Question

Write the unit vector in the direction of $\vec{\text{a}}=3\hat{\text{i}}+2\hat{\text{j}}+6\hat{\text{k}}$.

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Answer

We have,

$\vec{\text{a}}=3\hat{\text{i}}+2\hat{\text{j}}+6\hat{\text{k}}$

$|\vec{\text{a}}|=\sqrt{3^2+(-2)^2+6^2}$

$=\sqrt{9+4+36}$

$=\sqrt{49}$

$=7$

$\therefore$ Unit vector in the direction of $\vec{\text{a}}=\hat{\text{a}}=\frac{\vec{\text{a}}}{|\vec{\text{a}}|}=\frac{1}7\big(3\hat{\text{i}}-2\hat{\text{j}}+6\hat{\text{k}}\big)=\frac{3}7\hat{\text{i}}-\frac{2}7\hat{\text{j}}+\frac{6}7\hat{\text{k}}$

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