Two vectors

1. Jul 30, 2009

vorcil

Two particles move through space in a way that at time t, they are traveling in directions

(t-6,-t,6) And (1,2,1-t)
at what time are their directions parallel?

-

I know that for them to be parallel, a = Kb, where a and b are the two vectors, and one vector is a scalar of the other

I get something along the lines of

(t-6,-t,6) = K(1,2,1-t)
giving me equations
t-6 = k
-t = 2k
6 = k(1-t)

(-t/2) = k

subbing into t-6

t-6 = (-t/2)
2(t-6) = -t
2t - 12 = -t
3t = 12
12/3 = t
t=4

is this right?

2. Jul 30, 2009

Staff: Mentor

This is easy to check. Substitute t = 4 into your two vectors. If this value of t is correct, one vector will be a scalar multiple of the other (and vice versa, but the scalar multiple in this case will be the reciprocal of the other).

3. Jul 30, 2009

vorcil

so it's right?

4. Jul 30, 2009

Staff: Mentor

5. Jul 30, 2009

vorcil

(-2,-4,6)=k(1,2,-3)

-2=k*1, k = -2
-4=k*2 k = -4/2 = -2
6=k*(-3) k = 6/(-3) = -2

so yeah

awesome sauce
cheers bigears

6. Jul 30, 2009

Staff: Mentor

Good work! And you did it all yourself!