If A-B-B-A- then the angle between A and B is

( A×B )= ( B×A ) ⇒ ( A×B ) ( B×A )=0 [ ∵ ( B×A )= ( A×B ) ] ⇒ ( A×B )+ ( A×B )=0 ⇒ 2 ( A×B )=0 |2 ( A×B )|=|0| ⇒ nbsp; 2AB sinθ=0 [ ∵ | A |=A ≠ 0, | B | ...

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Byju's Answer

Standard XIII

Physics

Multiplication with Vectors

If A×B=B×A, t...

Question

If $\to A \times \to B = \to B \times \to A$ , then the angle between $\to A$ and $\to B$ is

π

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\frac{π}{3}

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\frac{π}{2}

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\frac{π}{4}

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Solution

The correct option is A $π$
$(\to A \times \to B) = (\to B \times \to A)$
$\Rightarrow (\to A \times \to B) - (\to B \times \to A) = \to 0$
$[∵ (\to B \times \to A) = - (\to A \times \to B)]$

$\Rightarrow (\to A \times \to B) + (\to A \times \to B) = \to 0$

$\Rightarrow 2 (\to A \times \to B) = \to 0$
$∣ ∣ ∣ 2 (\to A \times \to B) ∣ ∣ ∣ = ∣ ∣ ∣ \to 0 ∣ ∣ ∣$
$\Rightarrow 2 A B sin θ = 0$
$[∵ ∣ ∣ ∣ \to A ∣ ∣ ∣ = A \neq 0, ∣ ∣ ∣ \to B ∣ ∣ ∣ = B \neq 0]$
$\Rightarrow sin θ = 0$
$∴ θ = 0$ or $π$
Hence option $(a)$ is correct.

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Multiplication with Vectors

Standard XIII Physics

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If $\to A \times \to B = \to B \times \to A$ , then the angle between $\to A$ and $\to B$ is