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Vector Component

Given that ...

Question

Given that $\to A + \to B = \to R$ and $A^{2} + B^{2} = R^{2}$ .The angle between $\to A$ and $\to B$ is

A

0

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B

π / 4

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C

π / 2

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D

π

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Solution

The correct option is C $π / 2$
$R^{2} = A^{2} + B^{2} + 2 A B cos θ$
$\Rightarrow c o s θ = \frac{R^{2} - A^{2} - B^{2}}{2 A B} = \frac{R^{2} - R^{2}}{2 A B} = 0$
$∴ θ = π / 2$

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