Find the angle between (over {OP}) = ((^{-3}_{-4})) and (over{OQ}) = ((^8_{-15}))

Find the angle between (over {OP}) = ((^{-3}_{-4})) and (over{OQ}) = ((^8_{-15}))

Explanation

|(over{OP})| = (sqrt{(-3)^2 + (-4)^2}) = 5

|(over{OQ})| = (sqrt{(8)^2 +(-15)^2}) = 17

and |(over{OP})|.|(over{OQ})|  = ((^{-3}_{-4})).((^8_{15})) = -24 + 60 = 36

Then 36 = (5)(17) cos (theta) and finding cos (theta) = (frac{36}{85}) = 0.4235 and taking the inverse cosine to yield 

(theta) = cos(^{-1})(0.4235)

= 64.94(^o) 

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