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Question

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


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