Question

Find parametric equations for the line through the point (0, 1, 2) that is perpendicular to the line x - 1/t, y - 1/(2t), z - 2t, and intersects this line.

Answer 1

The parametric equations for the line through the point (0, 1, 2) that is perpendicular to the given line are x = -t, y = 1 - 2t, z = 2 - (1/2)t.

Step-by-step explanation:

To find the parametric equations for the line through the point (0, 1, 2) that is perpendicular to the line x - 1/t, y - 1/(2t), z - 2t, and intersects this line, we can determine the direction vector of the line x - 1/t, y - 1/(2t), z - 2t and take its negative reciprocal. The direction vector is (1, 1/2, -2) and its negative reciprocal is (-1, -2, -1/2). Let's call this vector A. Now, we can write the parametric equations as:

x = 0 + (-1)t

y = 1 + (-2)t

z = 2 + (-1/2)t