Ulyses A. answered • 02/22/21

UC Merced Grad For Physics and Math Tutor

First thing to do is find the vector associated with the line passing through the two points spoken.

A = (2,-1,3) = (x1,y1,z1)

B = (-1,4,0)

AB = < b1-a1, b2-a2, b3-a3>

AB = < -1-2, 4-(-1), 0-3>

AB = < -3, 5, -3> = < a,b,c>

Now as this vector passes through say Point A, this line can parameterized by the equations:

x = x1 + at

y = y1 + bt

z = z1 + ct

x = 2 - 3t

y = -1 + 5t

z = 3 - 3t

Feel free to correct me if I misspoke at any point. Hope this was helpful.