Chapter 6.4, Problem 43E

To determine

Whether u and v are orthogonal.

Answer to Problem 43E

Yes, u and v are orthogonal

Explanation of Solution

Given information:

  $\begin{array}{l}u=\left(10,-6\right)\\ v=\left(9,15\right)\end{array}$

Formula used: -

If $u.v=0$ , then u and are orthogonal

  $u.v=a_1{a}_2+b_1{b}_2$

  $\begin{array}{l}u.v=a_1{a}_2+b_1{b}_2\\ u.v=\left(10\right)\left(9\right)+\left(-6\right)\left(15\right)\\ u.v=90-90\\ u.v=0\end{array}$

Hence, u and v are orthogonal