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Question
Find a unit vector parallel to the vector \[\hat{i} + \sqrt{3} \hat{j}\]
Solution
Let \[\vec{a} = \hat{i} + \sqrt{3} \hat{j}\]
Then,
\[\left| \vec{a} \right| = \sqrt{1^2 + (\sqrt{3} )^2} = \sqrt{1 + 3} = \sqrt{4} = 2\]
Unit vector parallel to
\[\vec{a}\] = \[\hat{a} = \frac{\vec{a}}{\left| \vec{a} \right|} = \frac{1}{2}\left( \hat{i} + \sqrt{3} \hat{j} \right) = \frac{1}{2} \hat{i} + \frac{\sqrt{3}}{2} \hat{j}\]
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