Question

1) Find parametric equations for the line. (Use the parameter t.) the line through the points (−5, 2, 5) and (1, 9, −5) then x(t), y(t), z(t) =

Answer 1

The parametric equations for the line passing through the given points are x(t) = -5 + 6t, y(t) = 2 + 7t, and z(t) = 5 - 10t.

Step-by-step explanation:

To find the parametric equations for the line passing through the points (-5, 2, 5) and (1, 9, -5), we can use the formula:
x(t) = x0 + at
y(t) = y0 + bt
z(t) = z0 + ct

where (x0, y0, z0) are the coordinates of one of the points and (a, b, c) are the differences in the x, y, and z coordinates between the two points.

Substituting the values, we get:
x(t) = -5 + 6t
y(t) = 2 + 7t
z(t) = 5 - 10t