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

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

Concept:

Let two lines having direction ratio’s a1, b1, c1 and a2, 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

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