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Question

Question: The unit vector along \(\widehat{i} + \widehat{j}\) is...

The unit vector along i^+j^\widehat{i} + \widehat{j} is

A

k^\widehat{k}

B

i^+j^\widehat{i} + \widehat{j}

C

i^+j^2\frac{\widehat{i} + \widehat{j}}{\sqrt{2}}

D

i^+j^2\frac{\widehat{i} + \widehat{j}}{2}

Answer

i^+j^2\frac{\widehat{i} + \widehat{j}}{\sqrt{2}}

Explanation

Solution

R^=R→∣R∣=i^+j^12+12=12i^+12j^\widehat{R} = \frac{\overrightarrow{R}}{|R|} = \frac{\widehat{i} + \widehat{j}}{\sqrt{1^{2} + 1^{2}}} = \frac{1}{\sqrt{2}}\widehat{i} + \frac{1}{\sqrt{2}}\widehat{j}