Question

If `A = <3 ,8 ,8 >`, `B = <4 ,-3 ,-1 >` and `C=A-B`, what is the angle between A and C?

Answer 1

The angle is `=19.7`º

Explanation:

To calculate the angle between 2 vectors, we use the dot product.

`vecA.vecC=∥vecA∥*vecC∥*cos(vecA,vecC)`

`vecC=vecA-vecB=〈3,8,8〉-〈4,-3,-1〉=〈-1,11,9〉`

The dot product is

`vecA.vecC=〈3,8,8〉.〈-1,11,9〉=-3+88+72=157`

The modulus of `vecA` is

`∥vecA∥=∥〈3,8,8〉∥=sqrt(9+64+64)=sqrt137`

The modulus of `vecC` is

`∥vecC∥=∥〈-1,11,9〉∥=sqrt(1+121+81)=sqrt203`

Therefore,
`cos(vecA,vecC)=(vecA.vecC)/(∥vecA∥*∥vecC∥)`

`=157/(sqrt137sqrt203)=0.94`

`(vecA,vecC)=19.7`º