Question

Evaluate the expression: v ⋅ w Given the vectors: r = <8, 1, -6>; v = <6, 7, -3>; w = <-7, 5, 2>

Answer 1

The dot product is a scalar that is the sum of the product of the corresponding components.
For example,
<x1,y1,z1>.<x2,y2,z2> = x1x2+y1y2+z1z2  (scalar).

For v<6,7,-3> and w<-7,5,2>
we have
v.w=<6,7,-3>.<-7,5,2>=6(-7)+7(5)+(-3)(2)=-42+35-6=-13