t = 2a + 3b

u = 3a - b

v = a + 2b

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

Thanks.

Printable View

- Mar 25th 2010, 11:39 AMGAdamsGCSE vectors question
t = 2a + 3b

u = 3a - b

v = a + 2b

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

Thanks. - Mar 25th 2010, 12:05 PMrunning-gag
Hi

t+u+v = 6a + 4b

4t+*k*v = (8+k)a + (12+2k)b

are parallel if $\displaystyle \frac{8+k}{6} = \frac{12+2k}{4}$ - Mar 25th 2010, 12:18 PMGAdams
- Mar 25th 2010, 12:31 PMrunning-gag
t+u+v and 4t+

*k*v being parallel, there exists K such that t+u+v = K(4t+*k*v)

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)