Q. 9

# Find the distance between the planes x + 2y + 3z + 7 = 0 and 2x + 4y + 6z + 7 = 0.

Answer :

Formula : The distance between two parallel planes, say

Plane 1:ax + by + cz + d1 = 0 &

Plane 2:ax + by + cz + d2 = 0 is given by the formula

where () are constants of the planes

Therefore ,

First Plane x + 2y + 3z + 7 = 0

2(x + 2y + 3z + 7) = 0

2x + 4y + 6z + 14 = 0 …… (1)

Second plane 2x + 4y + 6z + 7 = 0 …… (2)

Using equation (1) and (2)

Distance between both planes

Rate this question :

Find the equation of the line passing through the point (–1, 3, –2) and perpendicular to the lines and

Mathematics - Board PapersFind the equation of the plane through the line of intersection of the planes x + y + z = 1 and 2x + 3y + 4z = 5 which is perpendicular to the plane x - y + z = 0. Also find the distance of the plane obtained above, from the origin.

**OR**

Find the distance of the point (2, 12, 5) from the point of intersection of the line and the plane

Mathematics - Board PapersFind the length of the perpendicular drawn from the origin to the plane 2x – 3y + 6z + 21 = 0.

Mathematics - Board PapersFind the coordinates of the foot of perpendicular and the length of the perpendicular drawn from the point P (5, 4, 2) to the line . Also find the image of P in this line.

Mathematics - Board PapersShow that the lines and intersect. Find their point of intersection.

Mathematics - Board Papers