# I need some help with vectors please

Kolika28

## Homework Statement

A(-4,-4), B(4,-2) and D(-2,2)
a) Determine AB and AD vector
b) A point C is determined by DC being parallel to AB and the angle ABC = 90. Calculate the coordinates of C.
I found out that C=(46/17, 54/17)
c) Another point E has the coordinates (t, 2t-1) where t = R
1) Find t so that point E is on line through C and D.

I am not able to solve this one

## Homework Equations

ED=k*CD
ED=(-2-t, -2t+1)
But I always end up with two unknown variables k and t.

## The Attempt at a Solution

ED=[-2-t,-2t+1]
ED must be parallel with CD, therefore is
ED=k*CD=[(-80/17)k,(-20/17)k]
I don't know what to do next

mattt
Actually, $$x=t ; y=2t-1$$ are the parametric equations of a straight line and they tell you that E is a point on this line. You just have to intersect this straight line, with the straight line the contains the vector DC (Do you know how to obtain the equations of this last straight line? )

Kolika28
Hmm, I'm not sure that I fully understand what you mean. I know how to find the parametic to DC, but what should I do with the two parametics?

mattt
Do you know how to obtain the equations (parametric, or vectorial, or any of the multiple type of equations of a straight line) of the unique straight line that passes through C and D ?

Kolika28
CD=[-2-(46/17), 2-(54/17)]=[-(80/17),-(20/17]
The parametric will then be
x=-2-(80/17)t
y=2-(20/17)t

mattt
Well, given that you already know that $$\vec{CD}$$ is parallel to vector $$\vec{AB}$$ and this last one is easier to calculate with, let us use it to form the equations of the unique straight line that passes through C and D. We can use the point $$D$$ and the vector $$\vec{AB}$$, so the parametric equations of that unique straight line are:

$$x=-2+8s; y=2+2s$$

Now you only have to obtain the point interesection of those two straight lines (this last one, and the one given by: $$x=t; y=2t-1$$ ). Do you know how to do this?

Kolika28
1.) -2+8s=t
2.) 2+2s=2t-1

1) s=(t+2)/8

2.) 2+2*((t+2)/8)=2t-1
t=2

mattt
Good, so you now know that t=2, then, in $$x=t;y=2t-1$$ you insert $$t=2$$ and obtain $$E$$, but the most important thing (far beyond any calculation) is: did you understand the reasoning behind this calculation?

Kolika28
Yes, I actually did! To be honest, in the beginning I didn't think I would. After looking through it some times I understand it now. I am sorry, that I am slow learner, and it took some time for me to fully understand what you meant. I really do appriate your help! Thank you so much!

mattt
You're welcome! And you must know that at the beginning we all were kind of "slow" :-)

Kolika28
Haha, I will remember that :)