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If |P̅ + Q̅| = |P̅| = |Q̅| then the angle between P̅ and Q̅ is

This question was previously asked in
Navik GD 26 April 2025 Memory-Based Paper (Section I + II)
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  1. 0°
  2. 120°
  3. 60°
  4. 90°

Answer (Detailed Solution Below)

Option 2 : 120°
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Detailed Solution

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Calculation:

Given: |P + Q| = |P| = |Q|

Let the magnitude of both vectors be P (since |P| = |Q|).

Now use the formula for magnitude of the sum of two vectors:

|P + Q|² = P² + Q² + 2PQ cosθ

Since |P + Q| = P, we have:

P² = P² + P² + 2P² cosθ

Simplifying:

P² = 2P² + 2P² cosθ

⇒ 0 = P² (2 + 2 cosθ)

⇒ 2 + 2 cosθ = 0

⇒ cosθ = -1

⇒ θ = 120°

Correct Answer: Option (2) → 120°

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Latest Indian Coast Guard Navik GD Updates

Last updated on Jul 4, 2025

-> The Indian Coast Guard Navik GD Application Correction Window is open now. Candidates can make the changes in the Application Forms through the link provided on the official website of the Indian Navy.

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