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Determine the angle between q= <2, 6> and r= <-3, 4>.

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Solution

We are required to find the angles between two vectors.

We will use the formula


q.r=\lvert q\rvert\lvert r\rvert\cos\theta

where θ is the angle between the vectors


\begin{gathered} q.r=(2*-3)+(6*4) \\ q.r=18 \end{gathered}
\lvert{q}\rvert=√(2^2+6^2)=√(40)=6.3246
\lvert{r}\rvert=√((-3)^2+4^2)=√(25)=5

Plug in the values obtained into the formula


\begin{gathered} 18=6.3246*5*\cos\theta \\ \cos\theta=0.5692 \\ \theta=\cos^(-1)(0.5692) \\ \theta=55.3^0 \end{gathered}

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