Thread: 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?

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.

So...

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

So far is that right, or no?

I would write:



Now, since and are perpendicular, to what will we equate their dot product?

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

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?

Equal to 0 because they are orthogonal vectors??

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

2x+3y=0 ?

Great! Now, you have:

(1)

(2)

Solve this system to get and .

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

Yes, great work!

Thank you so much! (: