Answer: (i) (ii) ...

### Find the acute angle between the following planes: (i) and (ii) and .

Answer: (i) (ii)

### Find the value of λ for which the given planes are perpendicular to each other: (i) and (ii) and .

Answer: (i) For plane perpendicular, cos 900 = 0 (ii) For plane perpendicular, cos 900 = 0 (λ × 1) + (2 ×...

### Show that the following planes are at right angles: (i) and (ii) and .

Answer: (i) (ii) = 6 + 24 – 30 = 30 – 30 = 0 = RHS Hence, the planes are...

### Find the acute angle between the following planes: (i) 2x – y + z = 5 and x + y + 2z = 7 (ii) x + 2y + 2z = 3 and 2x – 3y + 6z = 8

Answer: (i) The standard equation of plane, (ii) The standard equation of plane, ...

### Find the acute angle between the following planes: (i) x + y – z = 4 and x + 2y + z = 9 (ii) x + y – 2z = 6 and 2x – 2y + z = 11

Answer: (i) The standard equation of plane, (ii) The standard equation of plane, ...

### Show that each of the following pairs of planes are at right angles: (i) 3x + 4y – 5z = 7 and 2x + 6y + 6z + 7 = 0 (ii) x – 2y + 4z = 10 and 18x + 17y + 4z = 49

Answer: (i) if θ = 900 then cos 900 = 0 A1A2 + B1B2 + C1C2 = 0 By comparing with the standard equation of a plane, A1 = 3, B1 = 4, C1 = -5 A2 = 2, B2 = 6, C2 = 6 LHS = A1A2 + B1B2 + C1C2 = (3 × 2) +...

### 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) ...