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Applications of Cross Product

If the magnit...

Question

If the magnitude of vectors $\to A$ , $\to B$ and $\to C$ are 12, 5 and 13, respectively and $\to C = \to A + \to B$ , then the angle between the vectors $\to A$ and $\to B$ is

A

π / 4

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B

π / 3

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C

π / 2

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D

zero

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Solution

The correct option is B $π / 2$
Given:
$\to C = \to A + \to B$
$\to C . \to C = (\to A + \to B) . (\to A + \to B)$
$C^{2} = A^{2} + B^{2} + 2 A B cos θ$
$13^{2} = 12^{2} + 5^{2} + 2 (12) (5) cos θ$
$cos θ = 0 \Rightarrow θ = π / 2$

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