Question

What is the dot product of `<1,5,-3 >` and `<-1,4,2 >`?

Answer 1

The dot product is `-13`.

Explanation:

Let us consider `[1,5,-3]` as `vecA=hati+5hatj-3hatk` and `[-1,4,2]` as `vecB=-hati+4hatj+2hatk`.
The dot product of `[1,5,-3]` and `[-1,4,2]` is `vecA.vecB`.
`vecA.vecB=a_1b_1+a_2b_2+a_3b_3`.
Substitute the given values we get,
`=>vecA.vecB=(1)(-1)+(5)(4)+(-3)(2)=-13`.