If a¯=4, b¯=5, a¯−b¯=3 and θ is angle between the vectors a¯ and b¯, then cot2θ=_____

a¯−b¯2=9 ⇒ cosθ=45⇒cotθ=43 ⇒ cot2θ=169

If a¯=4, b¯=5, a¯−b¯=3 and θ is angle between the vectors a¯ and b¯, then cot2θ=_____

a¯−b¯2=9 ⇒ cosθ=45⇒cotθ=43 ⇒ cot2θ=169

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If $|\bar{a}| = 4, |\bar{b}| = 5, |\bar{a} - \bar{b}| = 3$ and $θ$ is angle between the vectors $\bar{a}$ and $\bar{b},$ then $\cot^{2} θ =_____$

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$\frac{3}{4}$

$\frac{9}{16}$

$\frac{16}{9}$

$\frac{4}{3}$

answer is D.

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Detailed Solution

${|\bar{a} - \bar{b}|}^{2} = 9 \Rightarrow \cos θ = \frac{4}{5}$
$\Rightarrow \cot θ = \frac{4}{3} \Rightarrow \cot^{2} θ = \frac{16}{9}$

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If a¯=4, b¯=5, a¯−b¯=3 and θ is angle between the vectors a¯ and b¯, then cot2θ=_____

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If $|\bar{a}| = 4, |\bar{b}| = 5, |\bar{a} - \bar{b}| = 3$ and $θ$ is angle between the vectors $\bar{a}$ and $\bar{b},$ then $\cot^{2} θ =_____$