Yes, this is correct. At time t = 4, the two particles' directions are parallel.

[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)

please someone check

I had -t = 2k
(-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?

 

[Mark44]

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).

 

[vorcil]

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).

so it's right?

 

[Mark44]

What does your check show?

 

[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

 

[Mark44]

Good work! And you did it all yourself!