Question

Find the distance between the line x-1/2 = y-1/-2 = z-2/3 and the plane 3x-2y-5=0

Answer 1

Answer:

Step-by-step explanation:

Distance from point to plane

 

Here's a quick sketch of how to calculate the distance from a point P=(x1,y1,z1) to a plane determined by normal vector N=(A,B,C) and point Q=(x0,y0,z0). The equation for the plane determined by N and Q is A(x−x0)+B(y−y0)+C(z−z0)=0, which we could write as Ax+By+Cz+D=0, where D=−Ax0−By0−Cz0.

This applet demonstrates the setup of the problem and the method we will use to derive a formula for the distance from the plane to the point P.