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