If -a-b-2 - a-b2 - 144 and -a- - 4- then -b- -

The correct option is C 3Using the definition of cross and dot products #160; |a⃗|^2|b⃗|^2sin^2θ+|a⃗|^2|b⃗|^2cos^2θ=144 ⇒ |a⃗|^2|b⃗|^2(sin^2θ+cos^2θ ...

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Standard XII

Mathematics

Product of Trigonometric Ratios in Terms of Their Sum

If |a×b|2 +...

Question

If $| \to a \times \to b |^{2} + (\to a \cdot \to b)^{2} = 144$ and $| \to a | = 4$ , then $| \to b | =$

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Solution

The correct option is C 3
Using the definition of cross and dot products
$| \to a |^{2} | \to b |^{2} {sin}^{2} θ + | \to a |^{2} | \to b |^{2} {cos}^{2} θ = 144$
$\Rightarrow | \to a |^{2} | \to b |^{2} ({sin}^{2} θ + {cos}^{2} θ) = 144$
$\Rightarrow 4^{2} | \to b |^{2} (1) = 144$
$\Rightarrow | \to b |^{2} = \frac{144}{16} = 9$
$∴ | \to b | = 3$

Note: $| \to a \times \to b | = | \to a | \to b | sin θ$
and $\to a \cdot \to b = | \to a | | \to b | cos θ$

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If |→a×→b|2+(→a⋅→b)2=144 and |→a|=4, then |→b|=

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