Question

If `A = <6 ,1 ,5 >`, `B = <3 ,6 ,-2 >` and `C=A-B`, what is the angle between A and C?

Answer 1

The angle is `=48º`

Explanation:

Let's calculate `vecC=vecA-vecB=〈6,1,5〉-〈3,6,-2〉`
`=〈3,-5,7〉`
To calculate the angle `theta`, we need to calculate the dot product.
`vecA.vecC=∥vecA∥*∥vecC∥costheta`
Let's calculate the dot product `vecA.vecC`
`=〈6,1,5〉.〈3,-5,7〉=18-5+35=48`
The modulus of `vecA=∥vecA∥=∥〈6,1,5〉∥`
`=sqrt(36+1+25)=sqrt62`
The modulus of `vecC=∥vecC∥=∥〈3,-5,7〉∥`
`=sqrt(9+25+49)=sqrt83`

`:. costheta=48/(sqrt62*sqrt83)=0.67`

`theta=48º`