Question

Can u please help me solve this problem

Answer 1

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

`(4,8)`

And the terminal point:

`(-12,14)`

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:

`||u||=√(x^2+y^2)`

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: