Question

Find the vector and parametric equations of the following lines.

a. The line parallel to the vector (2, -10) and passing through point P(1, -1, 3).
b. The line passing through point P(3, -1, 4) and point Q(3, -1, 5).

Answer 1

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

Step-by-step explanation:

To find the vector and parametric equations of a line, we need to consider two things: the direction vector and a point on the line.

a. For the line parallel to the vector (2, -10) and passing through point P(1, -1, 3):

The direction vector is (2, -10). The parametric equations are x = 1 + 2t, y = -1 - 10t, and z = 3.

b. For the line passing through points P(3, -1, 4) and Q(3, -1, 5):

The direction vector is (0, 0, 1) because the line is parallel to the z-axis. The parametric equations are x = 3, y = -1, and z = 4 + t.