First slide

Vectors

Question

If vectors A and B have an angle $θ$ between them, then value of $| \hat{A} - \hat{B} |$ will be

Moderate

A

$2 \cos \frac{θ}{2}$
B

$2 \tan \frac{θ}{2}$
C

$2 \sin \frac{θ}{2}$
D

None of these

Solution

$| \hat{A} - \hat{B} | = \sqrt{1 + 1 - 2 \times 1 \times 1 \times \cos θ} = 2 \sin \frac{θ}{2}$
Angle between $\hat{A}$ and $\hat{B}$ is also $θ$ , but their magnitudes are 1.

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