Question

Part B of this question please help all work shown thank you!

Answer 1

Solution

The vector u = PQ has initial point P(2, 14) and Q(7,3) and

The vector v = RS has initial point R(29, 8) and (12, 17)

For linear form

$y_2-y_1,x_2-x_1$

$\begin{gathered} \bar{U}=(7-2,3-14) \\ =(5,-11) \\ \bar{V}=(12-29,17-8) \\ =(-17,9) \end{gathered}$

Part A

$\begin{gathered} \bar{U}=5i-11j \\ \bar{V}=-17i+9j \end{gathered}$

Part B

$\begin{gathered} \theta=\tan ^{-1}(-\frac{11}{5})=-65.56^0 \\ \bar{U}=(\sqrt[]{146}\cos (-65.56),\sqrt[]{146}\sin (-65.56) \\ \gamma=\tan ^{-1}(-\frac{9}{17})+180^0=152.10^0 \\ \bar{V}=(\sqrt[]{370}\cos (152.1),\sqrt[]{370}sin(152.1) \end{gathered}$

Part C

$\begin{gathered} 7\bar{U}-4\bar{V} \\ 7(5,-11)-4(-17,9) \\ (35,-77)-(-68,36) \\ (35+68,-77-36) \\ (103,-113 \\ so \\ 7\bar{U}-4\bar{V}=(103,-113) \end{gathered}$