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Angle between Two Vectors

If a⃗, b⃗, √3...

Question

If $\to a, \to b, \sqrt{3} \to a - \to b$ are unit vectors, then acute angle between the vectors $\to a$ and $\to b$ is

A

$π / 2$

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B

$π / 4$

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C

$π / 3$

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D

$π / 6$

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Solution

The correct option is D
$π / 6$

$∣ \to a ∣= 1, ∣ \to b ∣= 1, ∣ \sqrt{3} \to a - \to b ∣= 1$

$∣ \sqrt{3} \to a - \to b ∣^{2} = 3 ∣ \to a ∣^{2} + ∣ \to b ∣^{2} - 2 \sqrt{3} \to a . \to b \Rightarrow \to a . \to b = \frac{\sqrt{3}}{2} \Rightarrow cos θ = cos (30 °) \Rightarrow θ = \frac{π}{6}$

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