# Determining whether three points lie on a straight line in three dimension

by k1point618
Tags: determining, dimension, line, points, straight
 P: 25 1. The problem statement, all variables and given/known data Determine whether the points lie on straight line A(2, 4, 2) B(3, 7, -2) C(1, 3, 3) 2. Relevant equations 3. The attempt at a solution I've looked up at the equation for lines in three dimension, and it appears to be x=x_0+at y=y_0+bt z=z_0+ct i tried to take the x y z for A and B and try to solve for a, b, c. Then if the same a, b, c work for BC, then ABC is on a line. That is my thought, but i can't manage to do the first part. I don't know how to use the information given and the equations to start with... Anyone please help me with this. This is my first time working with 3-dimensional coordinate system...
 HW Helper Sci Advisor Thanks P: 24,510 You don't have to work all that hard to get the equation for the line. In vector form the equation is [x,y,z]=A+(B-A)*t. Do you see why that gives you [x,y,z]=A at t=0 and [x,y,z]=B at t=1?? Can you translate that into equations for x, y and z?
P: 25
 Quote by Dick In vector form the equation is [x,y,z]=A+(B-A)*t. Do you see why that gives you [x,y,z]=A at t=0 and [x,y,z]=B at t=1??
This part i understand.
But i'm still not sure about how to translate that in to equations for x, y and z.

HW Helper