If the planes r (2 i - j + k )=3 and r (4 i - j + k )=5 are parallel, then + =

Step-by-step solution

The position vector forms of the planes are r (2 i - j + k ) = 3 and r (4 i - j + k ) = 5 , with normal vectors n₁ = 2 i - j + k and n₂ = 4 i - j + k respectively. For planes to be parallel, their normals must be parallel, implying direction proportionality: 2 4 = - -1 = 1 Since 2 4 = 1 2 , equating the remaining ratios yields: - -1 = 1 2 = 1 2 1 = 1 2 = 2 The sum is + = 1 2 + 2 = 5 2 .