Question

If `A = <2 ,4 ,-9 >`, `B = <3 ,1 ,-5 >` and `C=A-B`, what is the angle between A and C?

Answer 1

The angle is `26.1º`

Explanation:

To determine the angle `theta` two vectors, we use the dot product definition:
`vecA.vecC=∥vecA∥*∥vecC∥costheta`
Where `∥vecA∥` is the modulus of vector `vecA`

So, `costheta=(vecA.vecC)/(∥vecA∥*∥vecC∥)`
`vecC=vecA-vecB=〈-1,3,-4〉`
The dot product `=〈2,4,-9〉.〈-1,3,-4〉=-2+12+36=46`

Modulus of `vecA=sqrt(4+16+81)=sqrt101`
Modulus of `vecC=sqrt(1+9+16)=sqrt26`
`costheta=46/(sqrt101*sqrt26)=0.898`
`theta=26.1º`