Determine which pairs of lines are parallel or perpendicular.

Question

x = 1-3t, y = 7+4t
x = 2-4s, y = -3s

L1: r = (1,7) + t(-3,4)
L2: r = (2,-3) + t(-4,-3)

Now how is that perpendicular? I know how to find it a vector of a line is parallel but I don't know how to find out if it's perpendicular.

Answer 1

I assume you are talking about an x,y plot. You have to eliminate the parameters t or s to see how x and y are related.

For the first pair of lines; line 1

t = (1-x)/3
y = 7 + (4/3)(1-x) = 28/3 - (4/3)x

For the other line,
s = (2-x)/4
y = -(3/4)(2-x) = (3/4)x -3/2

Those two lines are perpendicular, because the products of their slopes is -1.

I assume the other pair of lines is parallel, but I am unfamiliar with the (r,t) representation.