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20 votes
20 votes
Can u please help me solve this problem

Can u please help me solve this problem-example-1
User Rohn Edwards
by
2.4k points

1 Answer

19 votes
19 votes

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:

User Victor Leal
by
3.3k points
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