Question
Find unit vector in the direction of vector $\vec{a}=2 \hat{i}+3 \hat{j}+\hat{k}$
✓
Answer
The unit vector in the direction of a vector $\vec a$ is given by $\hat{a}=\frac{1}{|\vec{a}|} \vec{a}$
Now $|\vec{a}|=\sqrt{2^{2}+3^{2}+1^{2}}=\sqrt{14}$
Therefore $\hat{a}=\frac{1}{\sqrt{14}}(2 \hat{i}+3 \hat{j}+\hat{k})=\frac{2}{\sqrt{14}} \hat{i}+\frac{3}{\sqrt{14}} \hat{j}+\frac{1}{\sqrt{14}} \hat{k}$
Now $|\vec{a}|=\sqrt{2^{2}+3^{2}+1^{2}}=\sqrt{14}$
Therefore $\hat{a}=\frac{1}{\sqrt{14}}(2 \hat{i}+3 \hat{j}+\hat{k})=\frac{2}{\sqrt{14}} \hat{i}+\frac{3}{\sqrt{14}} \hat{j}+\frac{1}{\sqrt{14}} \hat{k}$
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