If the angle between two lines whose d.rs are 1, 2, p − 1 and -3, 1, 2 is 90°, then p is

Question

Question

Answer 1

Concept:

Let two lines having direction ratio’s a_1, b₁, c₁ and a_2, b₂, c₂ respectively.

Condition for perpendicular lines: a₁a₂ + b₁b₂ + c₁c₂ = 0

Calculation:

Direction ratio’s of two lines are given as 1, 2, p − 1 and -3, 1, 2

Lines are perpendicular,

∴ 1 × -3 + 2 × 1 + (p – 1) × 2 = 0

⇒ -3 + 2 + 2p – 2 = 0

⇒ 2p = 3

∴ p = 3/2