Verify that the plane with equation x-2y+2z=6 is parallel to the plane with equation
r. (1,-2,2)=4

Find the perpendicular distances from the origin to each plane, and hence find the perpendicular distance between the planes.

Question

Verify that the plane with equation x-2y+2z=6 is parallel to the plane with equation 
r. (1,-2,2)=4

Find the perpendicular distances from the origin to each plane, and hence find the perpendicular distance between the planes.

experimentx · Answer

both have same direction cosine for normal, ie 1/3, -2/3, 2/3

anonymous · Answer

Ok, true. but what of the second part?

experimentx · Answer

takes time ... solve (normal from origin 0 0 0) x/1 = y/-2 = z/2 = k  and x-2y+2z=6 

you will get another point, find distance between origin and this point

similarly solve same line with  (1,-2,2)=4, find the distance between this point and origin ... 

subtract latter from former

experimentx · Answer

a lot better way than mine is given here http://www.math.ucla.edu/~ronmiech/Calculus_Problems/32A/chap11/section5/718d65/718_65.html

experimentx · Answer

more like distance formula between point and line in 2d geometry

anonymous · Answer

thanks