Find the angle between the vectors a = (3, 1, -2) and b (-2, 3,4).

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Solution

We know that angle between two vectors is given by -

$θ = {cos}^{- 1} \frac{a . b}{| a | | b |}$

$a . b = (3, 1, - 2) . (- 2, 3, 4) = - 6 + 3 - 8 = - 11$

$| a | = \sqrt{3^{2} + 1^{2} + 2^{2}} = \sqrt{14}$

$| b | = \sqrt{2^{2} + 3^{2} + 4^{2}} = \sqrt{29}$

$⟹ θ = {cos}^{- 1} \frac{- 11}{\sqrt{14} \sqrt{29}}$

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