Question

I got this problem on my homework wrong so I would like some help, I also added some of the formulas we use so hopefully that helps!

Answer 1

`\begin{gathered} v=10i-3j \\ w=-5i-j \end{gathered}`

First we need to find the dot product and the magnitude of each vector, so:

`\begin{gathered} \mleft\Vert v\mright||=\sqrt[]{10^2+(-3)^2}=\sqrt[]{109} \\ \mleft\Vert w\mright||=\sqrt[]{(-5)^2+(-1)^2}=\sqrt[]{26} \end{gathered}`
`v\cdot w=10\cdot(-5)+(-3)\cdot(-1)=-50+3=-47`

Therefore:

`\begin{gathered} \theta=\cos ^(-1)(\frac{-47}{\sqrt[]{109}\cdot\sqrt[]{26}}) \\ \theta\approx152.0^(\circ) \end{gathered}`