Find a unit vector in the direction of the vector a =3 i -2 j +6 … - Vidyadip

Question

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

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Answer

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

Then,

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

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

$=\sqrt{49}$

$=7$

$\therefore$ Unit vector $=\frac{\vec{\text{a}}}{|\vec{\text{a}}|}=\frac{3\hat{\text{i}}-2\hat{\text{j}}+6\hat{\text{k}}}7$

$=\frac{3}7\hat{\text{i}}-\frac{2}7\hat{\text{j}}+\frac{6}7\hat{\text{k}}$

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