Final answer:
To find the parametric equations for the line passing through two points, we can use the formula x = x1 + at, y = y1 + bt, and z = z1 + ct, where (x1, y1, z1) represents one point on the line and (a, b, c) represents the direction vector. Using the points (-5, 2, 5) and (1, 9, -6), the direction vector is calculated as a=6, b=7, and c=-11, resulting in the parametric equations x = -5 + 6t, y = 2 + 7t, and z = 5 - 11t.
Step-by-step explanation:
To find parametric equations for the line passing through the points (-5, 2, 5) and (1, 9, -6), we can use the formula:
x = x1 + at
y = y1 + bt
z = z1 + ct
where (x1, y1, z1) represents one point on the line, and (a, b, c) represents the direction vector of the line.
Using the given points (-5, 2, 5) and (1, 9, -6), we can calculate the direction vector:
a = (x2 - x1) = (1 - (-5)) = 6
b = (y2 - y1) = (9 - 2) = 7
c = (z2 - z1) = (-6 - 5) = -11
Therefore, the parametric equations for the line are:
x = -5 + 6t
y = 2 + 7t
z = 5 - 11t