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Work Done as Dot Product

Obtain the an...

Question

Obtain the angle between $\to A + \to B$ and $\to A - \to B$ if $\to A = 2^i + 3^j$ and $\to B =^i - 2^j .$

A

{cos}^{- 1} (\frac{4}{\sqrt{65}})

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B

π - {cos}^{- 1} (\frac{4}{\sqrt{65}})

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C

{sin}^{- 1} (\frac{4}{\sqrt{65}})

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D

- {sin}^{- 1} (\frac{4}{\sqrt{65}})

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Solution

The correct option is A ${cos}^{- 1} (\frac{4}{\sqrt{65}})$
$\to A = 2^i + 3^j \to B =^i - 2^j \to A + \to B = 3^i +^j \to A - \to B =^i + 5^j ∠ (\to A + \to B) (\to A - \to B) = θ cos θ = \frac{(\to A + \to B) \cdot (\to A - \to B)}{∣ ∣ ∣ \to A + \to B ∣ ∣ ∣ ∣ ∣ ∣ \to A - \to B ∣ ∣ ∣} = \frac{3 + 5}{\sqrt{10} \sqrt{26}} = \frac{8}{2 \sqrt{65}} = \frac{4}{\sqrt{65}}$

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