Chapter 4.4, Problem 10E

To determine

To find: The difference of the vectors.

Answer to Problem 10E

The difference of the vector is $\overline{JK}-\overline{LM}=\langle -1,-4\rangle$ .

Explanation of Solution

Given:

The given vectors is $J\left(6,7\right),K\left(10,-4\right),L\left(-2,8\right),M\left(3,1\right)$ .

The given equation is $\overline{JK}-\overline{LM}$ .

Calculation:

Consider the vertices are,

  $J\left(6,7\right),K\left(10,-4\right),L\left(-2,8\right),M\left(3,1\right)$

Then,

  $\begin{array}{l}J=\left[\begin{array}{c}6\\ 7\end{array}\right]\\ K=\left[\begin{array}{c}10\\ -4\end{array}\right]\\ L=\left[\begin{array}{c}-2\\ 8\end{array}\right]\\ M=\left[\begin{array}{c}3\\ 1\end{array}\right]\end{array}$

Consider the given equation is,

  $\overline{JK}-\overline{LM}$

Then,

  $\begin{array}{c}\overline{JK}-\overline{LM}=\left[\left[\begin{array}{c}10\\ -4\end{array}\right]-\left[\begin{array}{c}6\\ 7\end{array}\right]-\left[\left[\begin{array}{c}3\\ 1\end{array}\right]-\left[\begin{array}{c}-2\\ 8\end{array}\right]\right]\right]\\ =\left[\begin{array}{c}10-6\\ -4-7\end{array}\right]-\left[\begin{array}{c}3+3\\ 1-8\end{array}\right]\\ =\left[\begin{array}{c}4\\ -11\end{array}\right]-\left[\begin{array}{c}5\\ -7\end{array}\right]\\ =\left[\begin{array}{c}-1\\ -4\end{array}\right]\end{array}$

Thus, the solution is $\overline{JK}-\overline{LM}=\langle -1,-4\rangle$ .