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Question
Write a vector in the direction of vector \[5 \hat{i} - \hat{j} + 2 \hat{k}\] which has magnitude of 8 unit.
Solution
Given: \[\overrightarrow{a} =5 \hat{i} - \hat{j} + 2 \hat{k} \]
\[\left| \overrightarrow{a} \right| = \sqrt{5^2 + \left( - 1 \right)^2 + 2^{{}^2}}\]
\[= \sqrt{25 + 1 + 4} = \sqrt{30}\]
∴ Position Vector in the direction of vector
\[= 8 \times \frac{\overrightarrow{a}}{\left| \overrightarrow{a} \right|} = \frac{8}{\sqrt{30}}\left( 5 \hat{i} - \hat{j} + 2 \hat{k} \right)\]
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