Question

For what value of t are these two vectors parallel?

a) r = 4i + tj and s = 14i - 12j


What I Know: vectors are parallel if one is a scalar multiple of the other. I need to find a way that r and s relate by finding what number you can multiply r by to equal s.

What I Don't Know: How to approach the problem. How can 14i be related to 4i?

Answer 1

Never mind! I got it

Answer 2

LCM(4,14) = 28
So,

7r = 28i + 7tj
2s = 28i - 24j

so, if 7t = -24, 2s = 7r, so one is a multiple of the other.

Or, more directly,

14/4 r = 14i + 14/4 t j

so, if 14/4 t = -12, s is a multiple of r.

Answer 3

so you want:
(14, - 12) = k(4, t)
that is, 14 = 4k and -12 = kt

4k = 14
k = 14/4 = 7/2

then kt = -12
(7/2)t = -12
t = -12(2/7) = -24/7