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

Question

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

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Answer

The unit vector $\hat{a}$ in the direction of vector $\vec{a}=\hat{i}+\hat{j}+2\hat{k}$ is given by $\hat{a}=\frac{\vec{a}}{|a|}.$
$\Big|\vec{a}\Big|=\sqrt{1^2+1^2+2^2}=\sqrt{1+1+4}=\sqrt{6}$
$\therefore{\hat{a}}=\frac{\vec{a}}{\big|\vec{a}\big|}=\frac{\hat{i}+\hat{j}+2\hat{k}}{\sqrt{6}}=\frac{1}{\sqrt{6}}\hat{i}+\frac{1}{\sqrt{6}}\hat{j}+\frac{2}{\sqrt{6}}\hat{k}$

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