Question

SHOW THAT LINES (x-5)/-2 = (y+3)/4 = (z-1)/6 = t AND (x+2)/4 = (y-1)/-8 = (z+6)/-12 = t ARE PARALLEL.

Answer 1

(x-5)/-2 = (y+3)/4 = (z-1)/6 = t

(x-5)/-2 = t
x-5 = -2t
x = 5 - 2t
in the same way:
y = -3 + 4t
z = 1 + 6t, so the direction vector is (-2,4,6)

2nd line:
x = -2 + 4t
y = 1 - 8t
z = -6 - 12t , direction vector is (4,-8,-12) = -2(-2, 4, 6)
same direction, so they are parallel