Answer:
Given, \[\vec{a}=\hat{i}-\hat{j}+\hat{k}\] Now, unit vector in the direction of \[\vec{a}\] is \[\hat{a}=\frac{{\vec{a}}}{|\vec{a}|}=\frac{\hat{i}-\hat{j}+\hat{k}}{\sqrt{{{(1)}^{2}}+{{(-\,1)}^{2}}+(1)}}=\frac{\hat{i}-\hat{j}+\hat{k}}{\sqrt{3}}\] \[\therefore \] Vector of magnitude 8 units in direction of \[\hat{a}\] \[=\frac{8\,(\hat{i}-\hat{j}+\hat{k})}{\sqrt{3}}=\frac{8}{\sqrt{3}}\hat{i}-\frac{8}{\sqrt{3}}\hat{j}+\frac{8}{\sqrt{3}}\hat{k}\]
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