A line contains points P(32,-11,20) and Q(-18,-15,12). Write vector, parametric, and symmetric equations for this line.

Question

Please include steps and answers

Answer 1

Vector equation of this line: r = (32, - 11, 20) + t(- 18 - 32, - 15 + 11, 12 - 20); r(t) = (32, - 11, 20) + t(- 50, - 4, - 8). Then parametric equation: x = 32 - 50t, y = - 11 - 4t, z = 20 - 8t. By exluding parametr t we get symmetric equation of line: (x - 32)/(- 50) = (y + 11)/(- 4) = (z - 20)/(- 8) . After reducing denominators by (- 2) we get:

(x - 32)/25 = (y + 11)/2 = (z - 20)/4