Finding a scalar such that vectors p and q are parallel

[aero_zeppelin]

Homework Statement

Let:
p = (2,k)
q = (3,5)
Find k such that p and q are parallel

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

 

[Mark44]

Homework Statement

Let:
p = (2,k)
q = (3,5)
Find k such that p and q are parallel

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

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

 

[aero_zeppelin]

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

 

[HallsofIvy]

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

 

[Mark44]

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

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

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

 

[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.

 

[aero_zeppelin]

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

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

 

[Mark44]

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.

 

[aero_zeppelin]

great, thanks for the help!