Find parametric equations of lines through

Question

(-5, -6, 8) and (1, 3, 7) b. (10, 3, 1) and (6, -2, -3)

Answer 1

To find parametric equations of a line, we need a direction vector and a point on the line.

For the line through (-5, -6, 8) and (1, 3, 7):
1. Find the direction vector:
Let v be the vector from (-5, -6, 8) to (1, 3, 7).
v = (1 - (-5), 3 - (-6), 7 - 8)
= (6, 9, -1)

2. Choose a point on the line, say (-5, -6, 8). Let t be a parameter.
Therefore, the parametric equations for this line are:
x = -5 + 6t
y = -6 + 9t
z = 8 - t

For the line through (10, 3, 1) and (6, -2, -3):
1. Find the direction vector:
Let w be the vector from (10, 3, 1) to (6, -2, -3).
w = (6 - 10, -2 - 3, -3 - 1)
= (-4, -5, -4)

2. Choose a point on the line, say (10, 3, 1). Let s be a parameter.
Therefore, the parametric equations for this line are:
x = 10 - 4s
y = 3 - 5s
z = 1 - 4s