The angle between two vectors a- and b- with magnitudes -3 and 4- respectively and a-b-2 -3 isa 1-6b -3c -2d 5 -2

Here, |a|=√(3),|b|=4 and a.b=2√(3) [given] We know that, a.b=|a||b|cos θ ⇒ 2√(3)=√(3).4.cos θ ⇒ cos θ=2√(3)/4√(3)=1/2 ∴ θ=π/3 ...

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Byju's Answer

Standard XII

Physics

Vector Component

The angle bet...

Question

The angle between two vectors $\to a a n d \to b$ with magnitudes $\sqrt{3}$ and 4, respectively and $\to a . \to b = 2 \sqrt{3}$ is

(a) $\frac{π}{6}$

(b) $\frac{π}{3}$

(c) $\frac{π}{2}$

(d) $\frac{5 π}{2}$

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Solution

$H e r e, | \to a | = \sqrt{3}, | \to b | = 4 a n d \to a . \to b = 2 \sqrt{3} [g i v e n] We know that, \to a . \to b = | \to a | | \to b | c o s θ \Rightarrow 2 \sqrt{3} = \sqrt{3} .4 . c o s θ \Rightarrow c o s θ = \frac{2 \sqrt{3}}{4 \sqrt{3}} = \frac{1}{2} ∴ θ = \frac{π}{3}$

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