If a and b are unit vectors and θ is the angle between them, what is the maximum value of |a + b| + |a − b|? A. 2 B. 2√2 C. 4 D. 2√3 Answer: B) 2√2 Explanation: |a+b| = 2cos(θ/2) and |a−b| = 2sin(θ/2). Let f(θ) = 2cos(θ/2) + 2sin(θ/2). The maximum value of Acosx + Bsinx is √(A² + B²). So max value = √(2² + 2²) = √8 = 2√2.

imo class 12 vector algebra

If a and b are unit vectors and θ is the angle between them, what is the maximum value of |a + b| + |a − b|?

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If a and b are unit vectors and θ is the angle between them, what is the maximum value of |a + b| + |a − b|?

A. 2
B. 2√2
C. 4
D. 2√3

Answer: B) 2√2

Explanation: |a+b| = 2cos(θ/2) and |a−b| = 2sin(θ/2). Let f(θ) = 2cos(θ/2) + 2sin(θ/2). The maximum value of Acosx + Bsinx is √(A² + B²). So max value = √(2² + 2²) = √8 = 2√2.

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