Question

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

Answer 1

The scalar product of vectors is a real number, it is obtained by multiplying the respective components and adding them, that is:

`\begin{gathered} u= \\ v= \\ u\cdot v=u_1\cdot v_1+u_2\cdot v_2+\ldots+u_n\cdot v_n \end{gathered}`

So, in this case, you have

`\begin{gathered} v=<6,7,-3> \\ w=<-7,5,2> \\ v\cdot w=6\cdot-7+7\cdot5+-3\cdot2 \\ v\cdot w=-42+35-6 \\ v\cdot w=-13 \end{gathered}`

Therefore, the result of evaluating the expression is -13

`v\cdot w=-13`