Question

Find the distance from the point to the line.

(3, -1, 4) ; x = 4 - t, y = 3 + 2t, z = -5 + 3t
What is the distance?

Answer 1

To find the distance between a point and a line, use the formula: distance = |(Ax + By + C)| / sqrt(A2 + B2) where (x, y) is the point, and Ax + By + C = 0 is the equation of the line.

Step-by-step explanation:

To find the distance between a point and a line, we can use the formula:

distance = |(Ax + By + C)| / sqrt(A2 + B2)

where (x, y) is the point, and Ax + By + C = 0 is the equation of the line.

Using the given point (3, -1, 4) and the equation x = 4 - t, y = 3 + 2t, z = -5 + 3t, we can substitute the values into the formula:

distance = |(3(4 - t) + (-1)(3 + 2t) + 4(-5 + 3t))| / sqrt((32) + (-12) + 42).