Find the value of - a - b -2-A- a2-a-b-2B- a2 b2-a-b-2C- a2 b2-a-b-2D- a2-b2-2 a b

The correct option is B a^2b^2 (a.b)^2Let |a| = a, |b| = b and θ be the angle between them. nbsp; |a×b|^2 = (ab sin θ)^2 = a^2b^2 sin^2 θ = nbsp;(a^2b^2(1 ...

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Byju's Answer

Standard XII

Physics

Multiplication with Vectors

Find the valu...

Question

Find the value of $| \to a \times \to b |^{2} .$

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^{2} - b^{2} - 2 a b

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

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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.
$| \to a \times \to b |^{2} = (a b sin θ)^{2} = a^{2} b^{2} {sin}^{2} θ$
$= (a^{2} b^{2} (1 - {cos}^{2} θ) = a^{2} b^{2} - (a b cos θ)^{2}$
$= a^{2} b^{2} - (\to a . \to b)^{2}$

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Similar questions

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Find the value of |→a×→b|2.

The correct option is A a2b2−(→a.→b)2Let |→a|=a, →|b|=b and θ be the angle between them. |→a×→b|2=(ab sin θ)2=a2b2 sin2θ =(a2b2(1−cos2θ)=a2b2−(ab cos θ)2 =a2b2−(→a.→b)2

Find the value of $| \to a \times \to b |^{2} .$