Question

# The unit vector along $$\hat{i} + \hat {j}$$ is:

A
^k
B
^i+^j
C
^i+^j2
D
^i+^j2

Solution

## The correct option is C $$\dfrac{\hat{i} + \hat {j}}{\sqrt 2}$$Unit vector along$$( i + j) is\dfrac {( i + j)}{| i + j|}$$ $$|i + j | \ is \ magnitude \ of ( i + j)$$ we know, i and j are perpendicular to each other So, $$|i + j| = \sqrt{i^2 + j^2 + 2 i j cos 90^o}$$$$\sqrt{ 1 + 1} = \sqrt{2}$$hence, unit vector along $$(i + j) is \dfrac{(i + j)}{√2}$$Physics

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