Two vectors are parallel if their cross product is 0?

[teffy3001]

the question is:

u = 9i-6j
and
v = 5i+bj

for what value of b would u-v point in the same direction as w = 7i-3j?

can anyone help me get started on this problem, I am not looking for answers just a little bit of help because I'm confused.. thanks

 

[Dick]

There's no 'b' in your problem statement. What is it?

 

[arunbg]

Dick, the b is in the v component. I missed it at first glance too.
Anyway teffy, what conditions do you know that tests if two vectors are parallel?

 

[teffy3001]

v=5i + bj

thats where the b is..

 

[Dick]

Ooops. Missed it. So u-v=4i+(-6-b)j. Now answer arunbg's question.

 

[teffy3001]

um that two vectors are parallel if their cross product is 0?...

 

[arunbg]

So what do you get when you take the cross product?

 

[teffy3001]

i think that's where my problem lies now...im not sure how to find that out.

 

[Dick]

That's one way. But in only really works in three dimensions. More generally vectors A and B point in the same direction if A=k*B for some k>0 (any nonzero k if you don't mind them pointing in opposite directions). So you could set the ratio of the components equal.

 

[teffy3001]

okay so then how do i find the value of b?

 

[Dick]

Write down expressions for the ratio of the i components and the ratio of the j components and set them equal.

 

[tiny-tim]

Pictures often help with vectors!

(Cross-product will work, but, as you've found out, it's not particularly easy, and there is a simpler way)

If you're stuck, it often helps to draw a picture.

You did head this as a vectors problem, rather than an algebra one.

So draw (only roughly) the two vectors you have to make parallel!

What trigonometric thing could you measue to check if they're parallel?