# Math Help - GCSE vectors question

1. ## GCSE vectors question

t = 2a + 3b
u = 3a - b
v = a + 2b

If (t+u+v) is parallel to (4t+kv), find the value of k.

Thanks.

2. Hi

t+u+v = 6a + 4b
4t+kv = (8+k)a + (12+2k)b

are parallel if $\frac{8+k}{6} = \frac{12+2k}{4}$

3. Originally Posted by running-gag
Hi

t+u+v = 6a + 4b
4t+kv = (8+k)a + (12+2k)b

are parallel if $\frac{8+k}{6} = \frac{12+2k}{4}$
I can see what you have done but can't see why you have divided
(8+k)a + (12+2k)b
by 6a and 4b respectively. Also, not sure why there is an equals sign in the last line.

Thanks.

4. t+u+v and 4t+kv being parallel, there exists K such that t+u+v = K(4t+kv)

This means 6a + 4b = K [(8+k)a + (12+2k)b]

[6 - K(8+k)]a = [- 4 + K(12+2k)]b

a and b being independent (or supposed so) this leads to
6 - K(8+k) = 0 and - 4 + K(12+2k) = 0

K = 6/(8+k) and K = 4/(12+2k)

therefore 6/(8+k) = 4/(12+2k)