# Homework Help: Finding a scalar such that vectors p and q are parallel

1. Oct 10, 2011

### aero_zeppelin

1. The problem statement, all variables and given/known data
Let:
p = (2,k)
q = (3,5)
Find k such that p and q are parallel

3. The attempt at a solution

Well, I know that for two vectors to be parallel we need to have p = kq.

I know the answer will be kind of obvious but I just can't get it lolll, any help please??

Thanks

2. Oct 10, 2011

### Staff: Mentor

What does it mean for two vectors (p and kq, here) to be equal?

3. Oct 11, 2011

### aero_zeppelin

Hummm.... They need to have the same magnitude and direction?

4. Oct 11, 2011

### HallsofIvy

(a, b) and (c, d) are parallel if and only if c/a= d/b.

5. Oct 11, 2011

### Staff: Mentor

And what does this say about the coordinates of the two vectors?

6. Oct 11, 2011

### robphy

Thinking geometrically...

HallsofIvy's statement (essentially a similar-triangles argument) is equivalent to requiring that the slopes are equal.
Alternatively, consider certain "products" involving vectors and their geometric interpretation.

7. Oct 11, 2011

### aero_zeppelin

That they must be equal also, I guess...

So... p = tq (I'm using "t" as the scalar multiplying q):
tq = 2/3 (3,5) = 2, 10/3

So --> p = (2, k) = (2, 10/3)

k = 10/3 ????

Is that the way to do it? (trying to match the numbers only) or is there a more "pro" approach to it? lolll

8. Oct 11, 2011

### Staff: Mentor

That's the answer you want.

You can check your answer, by confirming that q = <3, 5> and p =<2, 10/3> are multiples of one another.

9. Oct 12, 2011

### aero_zeppelin

great, thanks for the help!