3-D coordinate systems problem

[bochai]

Pleas help me with this exercises(this is not a homework):

Determine whether the points lie on a straight line.

a) A(5,1,3), B(7,9,-1), C(1,-15,11)

b) K(0,3,-4) L(1,2,-2), M(3,0,1)

Should I draw the graph, then find the slopes?
Or is there any other way to approach?
Pleas help!
By the way, I got straight A's for Calc I,II. and every body keep telling me that Calc III is easier compare to Calc II. but, I feel it's so hard, and I don't know what to do. can some one give me some advice?thanks.

 

[StatusX]

If they're on a line, the vectors seperating each pair of points are scalar multiples of each other.

 

[HallsofIvy]

The simplest way is to do just what you said: Find the slope of the line through A and B and the slope of the line through B and C. They are the same line if and only if they have the same slope. Same for the second problem. Since the problem doesn't require you to graph them, that's not necessary.