2019 WAEC Further Mathematics Theory Find the angle between \(\over {OP}\) = (\(^{-3}_{-4}\)) and \(\over{OQ}\) = (\(^8_{-15}\))

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

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