Let a-b and c be three unit vectors such that a-b-c-32b-c- If b is not parallel to c- then the angle between a and b is-

The correct option is D 5π6 a̅× #160; (b̅×c̅) = b̅(a̅.c̅) c̅(a̅.b̅) = √(3)2(b̅+c̅) ⇒a̅.c̅ = √(3)2 a̅.b̅ = √(3)2⇒ cos θ = √(3)2 ...

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Byju's Answer

Standard XII

Physics

Vectors and Its Types

Let a,b and...

Question

Let $\to a, \to b$ and $\to c$ be three unit vectors such that $\to a \times (\to b \times \to c) = \frac{\sqrt{3}}{2} (\to b + \to c)$ . If $\to b$ is not parallel to $\to c$ , then the angle between $\to a$ and $\to b$ is:

\frac{3 π}{4}

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\frac{π}{2}

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\frac{2 π}{3}

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\frac{5 π}{6}

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Solution

The correct option is D $\frac{5 π}{6}$
$¯ a \times (¯ b \times ¯ c) = ¯ b (¯ a . ¯ c) - ¯ c (¯ a . ¯ b)$
$= \frac{\sqrt{3}}{2} (¯ b + ¯ c)$
$\Rightarrow ¯ a . ¯ c = \frac{\sqrt{3}}{2}$
$¯ a . ¯ b = \frac{- \sqrt{3}}{2} \Rightarrow c o s θ = \frac{- \sqrt{3}}{2}$
$\Rightarrow θ = 150^{\circ}$

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Similar questions

Let $\to a, \to b, a n d \to c$ be three unit vectors such that $\to a \times (\to b \times \to c) = \frac{\sqrt{3}}{2} (\to b \times \to c) . I f \to b$ is not parallel to $\to c$ , then the angle between $\to a a n d \to b$ is :

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\to a, \to b

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Let $^a,^b a n d^c$ be three unit vectors such that
$^a \times (^b \times^c) = \frac{\sqrt{3}}{2} (^b +^c) .$ If
$^b$ is not parallel to $^c$ , then the angle between $^a$ and $^b$ is