I have the following problem
Two mobiles are traveling in the same direction on the line with this equation
(x + 3) / 10 = (y + 10) / 20 = (z -10) / -20
The mobile M1 start off at A(-3,-10,10) and is traveling at a speed of 6M/S, M2 start at B(7,10,-10) and his traveling at 3M/S. When are they going to meet?
I have found M1 and M2 equation
M1 : (-3,-10,10) + t(2,4,-4) where t is the elapsed time
M2 : (7, 10, -10) +t(1,2,-2)
I can easily see that they will cross when t = 10, but how can I find that with algebra?
They meet when all of the components agree. So you can write the equation for any component, $-3+2t=7+t, -10+4t=10+2t, 10+(-4)t=-10+(-2)t$ and solve any of them for $t$. You should get the same answer from any one you pick. If the $t$'s disagree, they do not in fact meet.