Can u please help me solve this problem

Question

asked Jan 25, 2023 224k views

1 Answer

Joe Healy · Answer 1 · 2023-01-31T15:28:52+0000

Given that the initial point of vector "u" is:

And the terminal point:

You need to find the Component Form of the vector with this formula:

$u=\langle x_2-x_2,y_2-y_1\rangle$

In this case:

$\begin{gathered} x_2=-12 \\ x_1=4 \\ y_2=14 \\ y_1=8 \end{gathered}$

Then, you get:

$u=\langle-12-4,14-8\rangle=\langle-16,6\rangle$

Find the Magnitude using this formula:

In this case:

$\begin{gathered} x=-16 \\ y=6 \end{gathered}$

Therefore, by substituting values and evaluating, you get:

$||u||=√((-16)^2+(6)^2)\approx17.088$

In order to find the direction of the vector "u", you need to use this formula:

$\theta=tan^(-1)((y)/(x))$

Then, when you substitute the values of "x" and "y" into the formula and evaluate, you get:

$\theta=tan^(-1)((6)/(16))\approx20.556°$

Hence, the answer is: