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Question
Find a vector in the direction of \[\overrightarrow{a} = 2 \hat{i} - \hat{j} + 2 \hat{k} ,\] which has magnitude of 6 units.
Solution
Given: \[\overrightarrow{a} = 2 \hat{i} - \hat{j} + 2 \hat{k} \]
\[\left| \vec{a} \right| = \sqrt{2^2 + \left( - 1 \right)^2 + 2^2} = \sqrt{4 + 1 + 4} = \sqrt{9} = 3\]
∴ Required Vector \[= 6 \times \frac{\overrightarrow{a}}{\left| \overrightarrow{a} \right|} = 6 \times \frac{\left( 2 \hat{i} - \hat{j} + 2 \hat{k} \right)}{3} = 4 \hat{i} - 2 \hat{j} + 4 \hat{k}\]
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