If - a -3 and - b -2- then the value of the expression 2- a - b -2-2- a - b -2 is

(2|a×b|)^2+(2|a·b|)^2 =4|a|^2|b|^2sin^2θ+4|a|^2|b|^2cos^2θ =4|a|^2|b|^2(sin^2θ+cos^2θ) nbsp; =4|a|^2|b|^2 nbsp; =4·9·4 (∵ |a|=3, |b|=2) =144 nbsp; ...

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Byju's Answer

Standard XII

Physics

Multiplication with Vectors

If | a |=3 an...

Question

If $| \to a | = 3$ and $| \to b | = 2,$ then the value of the expression $(2 | \to a \times \to b |)^{2} + (2 | \to a \cdot \to b |)^{2}$ is _____

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Solution

$(2 | \to a \times \to b |)^{2} + (2 | \to a \cdot \to b |)^{2} = 4 | \to a |^{2} | \to b |^{2} {sin}^{2} θ + 4 | \to a |^{2} | \to b |^{2} {cos}^{2} θ = 4 | \to a |^{2} | \to b |^{2} ({sin}^{2} θ + {cos}^{2} θ) = 4 | \to a |^{2} | \to b |^{2}$
$= 4 \cdot 9 \cdot 4 (∵ | \to a | = 3, | \to b | = 2) = 144$

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If |→a|=3 and |→b|=2, then the value of the expression (2|→a×→b|)2+(2|→a⋅→b|)2 is _____

(2|→a×→b|)2+(2|→a⋅→b|)2=4|→a|2|→b|2sin2θ+4|→a|2|→b|2cos2θ=4|→a|2|→b|2(sin2θ+cos2θ)=4|→a|2|→b|2 =4⋅9⋅4 (∵|→a|=3, |→b|=2)=144

If $| \to a | = 3$ and $| \to b | = 2,$ then the value of the expression $(2 | \to a \times \to b |)^{2} + (2 | \to a \cdot \to b |)^{2}$ is _____