Attachment 25672

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

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

How do I find x and y?

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- Nov 12th 2012, 11:15 AMINeedOfHelpHelp finding a vector given two vectors?
Attachment 25672

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

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

How do I find x and y? - Nov 12th 2012, 11:22 AMMarkFLRe: 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*. - Nov 12th 2012, 11:30 AMINeedOfHelpRe: Help finding a vector given two vectors?
So...

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

2yj^{2}+4xi^{2}= -16

So far is that right, or no? - Nov 12th 2012, 11:37 AMMarkFLRe: 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? - Nov 12th 2012, 11:47 AMINeedOfHelpRe: Help finding a vector given two vectors?
B C

<2,1> * <2,3> = (4)+(3) = 7

That's not right, is it?

hdfhkfdg - Nov 12th 2012, 12:03 PMMarkFLRe: 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?

- Nov 12th 2012, 12:09 PMINeedOfHelpRe: Help finding a vector given two vectors?
Equal to 0 because they are orthogonal vectors??

- Nov 12th 2012, 12:11 PMMarkFLRe: Help finding a vector given two vectors?
Yes, exactly...good. So what equation results from this?

- Nov 12th 2012, 12:14 PMINeedOfHelpRe: Help finding a vector given two vectors?
2x+3y=0 ?

- Nov 12th 2012, 12:17 PMMarkFLRe: Help finding a vector given two vectors?
Great! (Cool) Now, you have:

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

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

Solve this system to get $\displaystyle x$ and $\displaystyle y$. - Nov 12th 2012, 12:26 PMINeedOfHelpRe: Help finding a vector given two vectors?
So would vector B = <-6,4> ?

- Nov 12th 2012, 12:29 PMMarkFLRe: Help finding a vector given two vectors?
Yes, great work!

- Nov 12th 2012, 12:29 PMINeedOfHelpRe: Help finding a vector given two vectors?
Thank you so much! (: