Exercise 28E

### Find the equation of the plane passing through the intersection of the planes x – 2y + z = 1 and 2x + y + z = 8, and parallel to the line with direction ratios 1, 2, 1. Also, find the perpendicular distance of (1, 1, 1) from the plane.

Answer: Cartesian form of equation of plane through the line of intersection of planes:                          ...

### Find the equation of the plane passing through the line of intersection of the planes 2x – y = 0 and 3z – y = 0, and perpendicular to the plane 4x + 5y – 3z = 0.

Answer: Cartesian form of equation of plane through the line of intersection of planes:                             The equation...

### Find the equation of the plane through the line of intersection of the planes x – 3y + z + 6 = 0 and x + 2y + 3z + 5 = 0, and passing through the origin.

Answer: Cartesian form of equation of plane through the line of intersection of planes: - x – 27y – 13z = 0 Multiplying by negative sign, x + 27y + 13z = 0 The equation of the plane is x + 27y + 13z...

### Find the equation of the planes passing through the intersection of the planes 2x + 3y – z + 1 = 0 and x + y – 2z + 3 = 0, and perpendicular to the plane 3x – y – 2z – 4 = 0.

Answer: Cartesian form of equation of plane through the line of intersection of planes:     The equation of the plane is 7x + 13y + 4z = 9.