The parametric equation of the line illustrates the independent variables x, y and z
The parametric equation of the line and direction is x = 5 + t; y = -1; z = 3 -2t
The question is incomplete, as the points and the lines are not given.
So, I will make use of the following assumed parameters:
The parametric equation of the line is represented as:
r<x,y,z> = Line + t<direction>
This gives
r<x,y,z> = (5, -1, 3) + t<1, 0, -2>
Express the equation in terms of x, y and z
x = 5 + t * 1
y = -1 + 0 * t
z = 3 -2 * t
Solve the equations
x = 5 + t
y = -1
z = 3 -2t
Hence, the parametric equation of the assumed line and direction is x = 5 + t; y = -1; z = 3 -2t
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