Question

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

Answer 1

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}`