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

Exercise 28E

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### 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.

### Find the equation of the plane through the line of intersection of the planes x + y + z = 6 and 2x + 3y + 4z + 5 = 0, and passing through the point (1, 1, 1).

Answer: Cartesian form of equation of plane through the line of intersection of planes: 14x + 14y + 14z – 84 + 6x + 9y + 12z + 15 = 0 20x + 23y + 26z...

### Find the equation of the plane passing through each group of points: (i) A (2, 2, -1), B (3, 4, 2) and C (7, 0, 6) (ii) A (0, -1, -1), B (4, 5, 1) and C (3, 9, 4)

Answer: (i) Given, A (2, 2, -1) B (3, 4, 2) C (7, 0, 6) ...