Chapter 6, Problem 19STP

To determine

To select:

The correct option of the dot product of vector $u=2i-2j$ and $v=3i-5j$

(A) $0$

(B) $16$

(C) $5i-7j$

(D) $6i+10j$

Answer to Problem 19STP

The correct answer is (D). The dot product of vector $u=2i-2j$ and $v=3i-5j$ is $6i+10j$

Explanation of Solution

Given information:

  $\begin{array}{l}u=2i-2j\\ v=3i-5j\end{array}$

Calculation:

The given vectors are:

  $\begin{array}{l}\left(u_1,u_2\right)=\left(2,-2\right)\\ \left(v_1,v_2\right)=\left(3,-5\right)\end{array}$

Now the dot product of vectors is calculated as:

  $\begin{array}{l}u\cdot v=\left(u_1\right)\left(v_1\right)i+\left(u_2\right)\left(v_2\right)j\\ u\cdot v=\left(3\right)\left(2\right)i+\left(-5\right)\left(-2\right)j\\ u\cdot v=6i+10j\end{array}$

so, correct option is (D).