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