Chapter 6.4, Problem 9E

To determine

To Find: Dot product of u and v.

Answer to Problem 9E

  $u.v=14$

Explanation of Solution

Given information:

  $\begin{array}{l}u=\left(5i+j\right)\\ v=\left(3i-j\right)\end{array}$

Formula used: -

  $u.v=a_1{a}_2+b_1{b}_2$

Where $u=\left(a_{1}i+b_{1}j\right)$ and $v=\left(a_{2}i+b_{2}j\right)$

  $u.v=a_1{a}_2+b_1{b}_2$

By using above formula:

  $\begin{array}{l}{a}_1=5,a_{{}_2}=3,b_1=1,b_2=-1\\ \\ u.v=\left(5\right)\left(3\right)+\left(1\right)\left(-1\right)\\ =15-1\\ \boxed{u.v=14}\end{array}$