Finding Distances to Lines and Planes in 3D Geometry

[mercedesbenz]

Homework Statement

1. please help me find the distance from the point (0, 0 ,0) to the line
$$x=4-t, y=3+2t, z=-5+3t (-\nfty<t<\infty)$$

2. find the distance between the point (3, 1, -2) and the plane $$x+2y-2z=4$$

3 find the principle unit notmal N, the curvature , and the radius of curvature for the plane curve $$r(t)=ti+(sint)j$$

Homework Equations

The Attempt at a Solution

 

[dx]

Show your attempt.

 

[HallsofIvy]

If we won't even try, we have no idea what methods would be appropriate!

Most calculus textbooks give FORMULAS for "distance to a line" and "distance to a plane". Can you use them?

Do you know how to find the line, through a point, perpendicular to a given point?

Do you know how to find the line, through a point, perpendicular to a given plane?

Do you understand why those would be useful for this problem?