Question

find parametric equations for the line through A(6,1,-2) and B(7,3,-3)

Answer 1

Any ideas?

Answer 2

Vector equation of a line passing through points A and B is: A + t(B - A)
A is the point on the line and (B - A) is the direction of the line.

If (x, y, z) is any point on the line, then:
<x, y, z> = <6, 1 , -2> + t<7-6, 3-1, -3+2>
<x, y, z> = <6, 1 , -2> + t<1, 2, -1>

x = 6 + t
y = 1 + 2t
z = -2 - t