If a, b, c are three mutually perpendicular vectors of equal magnitude, the angle which a + b + c makes with a is:

If a, b, c are three mutually perpendicular vectors of equal magnitude, the angle which a + b + c makes with a is:

• A. cos⁻¹(1/3)
• B. cos⁻¹(1/√3)
• C. cos⁻¹(1/√2)
• D. π/2

Answer: B) cos⁻¹(1/√3)

Explanation: Let magnitudes be m. |a+b+c| = √(m² + m² + m²) = m√3. a.(a+b+c) = a.a + a.b + a.c = m² + 0 + 0 = m². Angle cosθ = m² / (m × m√3) = 1/√3. Hence θ = cos⁻¹(1/√3).