# Thread: Vector help.

1. ## Vector help.

This is a quiz problem i had that i got wrong and i was hoping somebody could give me the correct answers to this problem..

The following points a=[0,2] b=[1,2] c=[0,0] d=[1,-2] form a trapezoid.

a). Make a graph of the figure.
b.) What are the vectors corresponding to the sides?
c.) What are the length of the sides?
d.) What is the measure of the angels in c?
e.) Find the vectors corresponding to the diagonals.
f.) Are the diagonals perpendicular?

I only got a & b correct.

2. Originally Posted by Aquameatwad
This is a quiz problem i had that i got wrong and i was hoping somebody could give me the correct answers to this problem..

The following points a=[0,2] b=[1,2] c=[0,0] d=[1,-2] form a trapezoid.

a). Make a graph of the figure.
b.) What are the vectors corresponding to the sides?
c.) What are the length of the sides?
d.) What is the measure of the angels in c?
e.) Find the vectors corresponding to the diagonals.
f.) Are the diagonals perpendicular?

I only got a & b correct.
Please show your answers to b and all your working for c, d, e and f.

3. i have no clue about e and f. i don't know if the rest are correct either.

4. What you have written doesn't make a whole lot of sense.
Your graph of the trapezoid is correct.

In b you are asked to find the vectors corresponding to the sides. You appear not to have done that or you have combined it with c which makes it very difficult to understand. You first have "$\displaystyle c= \begin{bmatrix}1 \\ 2\end{bmatrix}- \begin{bmatrix}0 \\ 2\end{bmatrix}= \begin{bmatrix}1 \\ 0\end{bmatrix}$ which is correct (although since the point [0, 0] is already labeled "c", you should not use the same letter to designate the vector) but then you have [b]that[b] equal to "$\displaystyle \sqrt{1^2}= 1$". A vector cannot be equal to a number! They are not the same thing.
The side from point a to point b is given by the vector $\displaystyle \begin{bmatrix}1 \\ 0\end{bmatrix}$. Same for the other- the problem asks for a vector not a number. After you have written the vectors for (b) you can find the lengths as you do.

(d) asks for "the measures of the angles in c". Does it really say "angles", plural? That makes no sense. There is only one angle at c. You first subtract points to get the two vectors, from c to a and from c to d. You should not need to do that. Those are vectors you have already found and called "b" and "d". You use the fact that [tex]u\cdot v= ||u||||v||cos(\theta)[/itex]. The dot product of the two vectors is (0)(1)+ (2)(-2)= -4, not -3! Their lengths are 2 and $\displaystyle \sqrt{5}$ as you have. But that is NOT the angle. What you have, with the numerator corrected, is $\displaystyle cos(\theta)= -\frac{2}{\sqrt{5}}$. You still need to find the angle itself. Either write just $\displaystyle \theta= cos^{-1}(-\frac{2}{\sqrt{5}})$ or use a calculator. And don't expect your teacher to guess your answer. Write specifically "The angle c is ..." or $\displaystyle \theta=$ where you already written that $\displaystyle \theta$ is the angle at c. And, if you really do write all over the paper like that, you should either underline or circle the answer to make sure your teacher knows what you intend as the answer.

For (e), you have already drawn one of the diagonals, from c to b. The other is from a to d. Subtract just as you did for the sides. For (f) they are perpendicular if and only if their dot product is 0.

Generally, you have done the calculations correctly. But make sure you label your answer- don't expect your teacher search your paper for them!