Question

Find the angle θ between the vectors the v= 5i - 3j and w= 2i - j. Round your answer to the nearest hundredth of a degree

Answer 1

Solution;

`\begin{gathered} v=5i-3j \\ w=2i-j \end{gathered}`
`\begin{gathered} v.w=\lvert{v}\rvert\lvert{w}\rvert cos\theta \\ cos\theta=\frac{v.w}{\lvert{v}\rvert\lvert{w}\rvert} \end{gathered}`
`\begin{gathered} v.w=5(2)+(-3)(-1)=10+3=13 \\ \lvert{v}\rvert=√(5^2+(-3)^2)=√(34) \\ \lvert{w}\rvert=√(2^2+(-1)^2)=√(5) \\ \end{gathered}`
`\begin{gathered} cos\theta=\frac{13}{(\sqrt{5)(√(34))}}=(13)/(13.03840481)=0.9971 \\ \theta=\cos^(-1)(0.9971) \\ \theta=4.40\degree \end{gathered}`

The answer is 4.40°