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Question: The expression \(\left( \frac{1}{\sqrt{2}}\widehat{i} + \frac{1}{\sqrt{2}}\widehat{j} \right)\) is a...

The expression (12i^+12j^)\left( \frac{1}{\sqrt{2}}\widehat{i} + \frac{1}{\sqrt{2}}\widehat{j} \right) is a

A

Unit vector

B

Null vector

C

Vector of magnitude 2\sqrt{2}

D

Scalar

Answer

Unit vector

Explanation

Solution

P→=12i^+12j^\overrightarrow{P} = \frac{1}{\sqrt{2}}\widehat{i} + \frac{1}{\sqrt{2}}\widehat{j}∴∣P→∣=(12)2+(12)2|\overrightarrow{P}| = \sqrt{\left( \frac{1}{\sqrt{2}} \right)^{2} + \left( \frac{1}{\sqrt{2}} \right)^{2}}= 1

∴ It is a unit vector.