The point (2, -1 , -8) is on the line and the expression (3, 9, 1) represents the family of vectors parallel to the line.
First, we have to find the vector expression of the line function based on the following parametric equations:
t = (x - 2) / 3 (1)
x = 3 · t + 2
t = (y + 1) / 9 (2)
y = 9 · t - 1
t = z + 8 (3)
z = t - 8
(x, y, z) = (2, - 1, - 8) + t · (3, 9, 1) (4)
The point (2, -1 , -8) is on the line and the expression (3, 9, 1) represents the family of vectors parallel to the line.
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