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Question
Write a unit vector in the direction of \[\overrightarrow{a} = 3 \hat{i} + 2 \hat{j} + 6 \hat{k} .\]
Solution
We have,
\[\overrightarrow{a} = 3 \hat{i} - 2 \hat{j} + 6 \hat{k} .\]
\[\left| \overrightarrow{a} \right| = \sqrt{3^2 + \left( - 2 \right)^2 + 6^2} = \sqrt{9 + 4 + 36} = \sqrt{49} = 7 \]
∴ Unit vector in the direction of \[\overrightarrow{a}\] = \[\widehat{a} = \frac{\overrightarrow{a}}{\left| \overrightarrow{a} \right|} = \frac{1}{7} \left( 3 \hat{i} - 2 \hat{j} + 6 \hat{k} \right) = \frac{3}{7} \hat{i} - \frac{2}{7} \hat{j} + \frac{6}{7} \hat{k}\]
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