First slide

Vectors

Question

If $\hat{a} and \hat{b}$ are unit vectors and if $|\hat{a} \times \hat{b}| = \sqrt{3} (\hat{a} \cdot \hat{b})$ , then the magnitude of the vector $(\hat{a} - \hat{b})$ is

Moderate

A

$2$
B

$1$
C

$\sqrt{3}$
D

$\sqrt{2}$

Solution

In the data, $|\hat{a} \times \hat{b}| = sinθ$ and $\hat{a} \cdot \hat{b} = cosθ$ . Using these gives $θ = 60^{o} .$ $|\hat{a} - \hat{b}| = \sqrt{1^{2} + 1^{2} - 2 \times 1 \times 1 \times \cos 60^{o}}$

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