If a and b are two non-zero vectors- -a-b-2 is equal to which of the following-

Let|a| = a, |b| = b and θ be the angle between them. |a×b|^2 = (ab sinθ )^2 = a^2 b^2 sin ^2 θ = a^2 b^2(1 cos^2 θ) = a^2b^2 (a.b cosθ)^2 = a^2b^2 (a.b)^2 ...

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Byju's Answer

Standard XI

Physics

Multiplication with Vectors

If a and b ar...

Question

If $\to a$ and $\to b$ are two non-zero vectors, $| \to a \times \to b |^{2}$ is equal to which of the following?

a^{2} b^{2} - (\to a . \to b)^{2}

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a^{2} b^{2} + (\to a . \to b)^{2}

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a b - (\to a . \to b)^{2}

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a^{2} b^{2} - (\to a . \to b)

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Solution

The correct option is A $a^{2} b^{2} - (\to a . \to b)^{2}$
Let $| \to a | = a, | \to b | = b$ and $θ$ be the angle between them.
$| \to a \times \to b |^{2} = (a b sin θ)^{2} = a^{2} b^{2} {sin}^{2} θ$
$= a^{2} b^{2} (1 - c o s^{2} θ) = a^{2} b^{2} - (a . b cos θ)^{2}$
$= a^{2} b^{2} - (\to a . \to b)^{2}$

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