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Concepts Of Physics MCQ Edition [Volume 1]
Exam
Concepts Of Physics MCQ Edition [Volume 1]
Subject
Physics
Chapter
Physics and Mathematics

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Physics and Mathematics

Two vectors have magnitudes of 3 unit and 4 unit, respectively....

Two vectors have magnitudes of 33 unit and 44 unit, respectively. Determine the angle between them if the magnitude of the resultant is 55 unit.

Options

  1. A60^{}^{{}^{\circ}}
  2. B0^{}^{{}^{\circ}}
  3. C180^{}^{{}^{\circ}}
  4. D90^{}^{{}^{\circ}}

Correct answer

D. 90^{}^{{}^{\circ}}

Step-by-step solution

Let the magnitudes of the two vectors be A=3A = 3 unit and B=4B = 4 unit.

Let the magnitude of the resultant vector be R=5R = 5 unit.

The magnitude of the resultant of two vectors is given by the formula:

R2=A2+B2+2ABcos⁡θR^2 = A^2 + B^2 + 2AB \cos \theta

Substituting the given values:

52=32+42+2(3)(4)cos⁡θ5^2 = 3^2 + 4^2 + 2(3)(4) \cos \theta

25=9+16+24cos⁡θ25 = 9 + 16 + 24 \cos \theta

25=25+24cos⁡θ25 = 25 + 24 \cos \theta

24cos⁡θ=024 \cos \theta = 0

cos⁡θ=0\cos \theta = 0

\theta = 90^{}^{{}^{\circ}}
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