If the angle between a and b is 2π/3 and the projection of a in the direction of b is -2 , then |a| is: - Mathematics MCQ Mathematics Mock Test - 1 2026 | ExamTest.live

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If the angle between a and b is \frac{2 π}{3} and the projection of a in the direction of b is - 2, then ∣ a ∣ is:

Solution & Step-by-step Explanation

The projection of a on b is given by: Proj_{b} a = ∣ a ∣ cos θ Given θ = \frac{2 π}{3} and Proj = - 2 : - 2 = ∣ a ∣ cos \frac{2 π}{3} Since cos \frac{2 π}{3} = - 1/2 : - 2 = ∣ a ∣ (- \frac{1}{2}) ∣ a ∣ = 4

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If the angle between a and b is \frac{2 π}{3} and the projection of a in the direction of b is - 2, then ∣ a ∣ is:

4

3

2

1

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