Question

Given v=−8i−5j and w=3i−j, find the angle between v and w.

Answer 1

Given:-

`v=-8i-5j,w=3i-j`

To find the angle between v and w.

So now we use the formula,

`cos\theta=(v.w)/(\left|w\right|\left|v\right|)`

So now we find the dot product of the given vectors. so we get,

`\begin{gathered} v.w=-8(3)+(5) \\ v.w=-24+5 \\ v.w=-19 \end{gathered}`

Also now we find the modulus values,

`\left|v\right|=√(8^2+5^2)=√(64+25)=√(89)`

Also,

`\left|w\right|=√(9+1)=√(10)`

Substituting we get,

`\theta=cos^(-1)(-(19)/(√(81)√(10)))`