# Help finding a vector given two vectors?

• Nov 12th 2012, 11:15 AM
INeedOfHelp
Help 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 AM
MarkFL
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.
• Nov 12th 2012, 11:30 AM
INeedOfHelp
Re: Help finding a vector given two vectors?
So...

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

So far is that right, or no?
• Nov 12th 2012, 11:37 AM
MarkFL
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?
• Nov 12th 2012, 11:47 AM
INeedOfHelp
Re: 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 PM
MarkFL
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?
• Nov 12th 2012, 12:09 PM
INeedOfHelp
Re: Help finding a vector given two vectors?
Equal to 0 because they are orthogonal vectors??
• Nov 12th 2012, 12:11 PM
MarkFL
Re: Help finding a vector given two vectors?
Yes, exactly...good. So what equation results from this?
• Nov 12th 2012, 12:14 PM
INeedOfHelp
Re: Help finding a vector given two vectors?
2x+3y=0 ?
• Nov 12th 2012, 12:17 PM
MarkFL
Re: 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 PM
INeedOfHelp
Re: Help finding a vector given two vectors?
So would vector B = <-6,4> ?
• Nov 12th 2012, 12:29 PM
MarkFL
Re: Help finding a vector given two vectors?
Yes, great work!
• Nov 12th 2012, 12:29 PM
INeedOfHelp
Re: Help finding a vector given two vectors?
Thank you so much! (: