Question

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IF C= A+B AND MAGNITUDE OF A , B AND C IS 12 , 5 AND 13 RESPECTIVELY , THE ANGLE BETWEEN A AND B IS ? ( A ,B AND C ARE ALL VECTORS )

Answer 1

Given that : A + B = C

Squaring on both sides we get :

⇒ (A + B)² = C²

⇒ A² + B² + 2(A.B) = C²

Given the Magnitudes of A = 12 and B = 5 and C = 13

⇒ 12² + 5² + 2(A.B) = 13²

⇒ 144 + 25 + 2(A.B) = 169

⇒ (A.B) = 0

We know that (A.B) = IAI × IBI × Cosθ (θ is the angle between the A and B Vectors)

⇒ IAI × IBI × Cosθ = 0

⇒ Cosθ = 0

⇒ θ = π/2

⇒ The Angle between the Vectors A and B is 90°