# Thread: Help finding a vector given two vectors?

1. ## Help finding a vector given two vectors?

Find the values of x and y and write vector B.

xi+yj * 4i + 2j = -16

How do I find x and y?

2. ## Re: Help finding a vector given two vectors?

Equate the dot product of A and B to -16, and to what should you equate the dot product of B and C?

Once you write these products, then you will two equations in x and y.

3. ## Re: Help finding a vector given two vectors?

So...

(yj)(2j)+(xi)(4i)= -16
2yj2+4xi2 = -16

So far is that right, or no?

4. ## Re: Help finding a vector given two vectors?

I would write:

$\displaystyle \vec{A}\cdot\vec{B}=\langle 4,2 \rangle \cdot \langle x,y \rangle=4x+2y=-16\,\therefore\,2x+y=-8$

Now, since $\displaystyle \vec{B}$ and $\displaystyle \vec{C}$ are perpendicular, to what will we equate their dot product?

5. ## Re: Help finding a vector given two vectors?

B C
<2,1> * <2,3> = (4)+(3) = 7
That's not right, is it?
hdfhkfdg

6. ## Re: Help finding a vector given two vectors?

No, that's not right...you are taking the dot product of one half of A and C...you want to use B and C, and set it equal to what?

7. ## Re: Help finding a vector given two vectors?

Equal to 0 because they are orthogonal vectors??

8. ## Re: Help finding a vector given two vectors?

Yes, exactly...good. So what equation results from this?

2x+3y=0 ?

10. ## Re: Help finding a vector given two vectors?

Great! Now, you have:

(1) $\displaystyle 2x+y=-8$

(2) $\displaystyle 2x+3y=0$

Solve this system to get $\displaystyle x$ and $\displaystyle y$.

11. ## Re: Help finding a vector given two vectors?

So would vector B = <-6,4> ?

12. ## Re: Help finding a vector given two vectors?

Yes, great work!

13. ## Re: Help finding a vector given two vectors?

Thank you so much! (: