Find a vector in the direction of ` vec a=2 hat i- hat j+2 hat k ,` which has magnitude of 6 units.

Explanation

`\vec{a}=2 \hat{i}-\hat{j}+2 \hat{k}`


`\hat{a}=\frac{\vec{a}}{|\vec{a}|}=\frac{2 \hat{i}-\hat{j}+2 \hat{k}}{\sqrt{2^{2}+(-1)^{2}+(2)^{2}}}`


`=\frac{2 \hat{i}-\hat{j}+2 \hat{k}}{\sqrt{9}}`


`=\frac{1}{3}(2 \hat{i}-\hat{j}+2 \hat{k})`


`\hat{b}=\frac{\vec{b}}{|\vec{b}|}=\frac{\vec{b}}{6}`


`\hat{b}=\hat{a}`


`=\frac{1}{3}(2 \hat{i}-\hat{j}+2 \hat{k})`


`\frac{1}{3}(2 \hat{i}-\hat{j}+2 \hat{k})=\frac{\hat{b}}{6}`


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