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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

3

unit and

4

unit, respectively. Determine the angle between them if the magnitude of the resultant is

1

unit.

Options

A $180^{}^{{}^{\circ}}$
B $0^{}^{{}^{\circ}}$
C $45^{}^{{}^{\circ}}$
D $90^{}^{{}^{\circ}}$

Correct answer

A. $180^{}^{{}^{\circ}}$

Step-by-step solution

Let the magnitudes of the two vectors be

A = 3

and

B = 4

, and the magnitude of their resultant be

R = 1

.

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

R^2 = A^2 + B^2 + 2AB \cos \theta

Substituting the given values:

1^2 = 3^2 + 4^2 + 2(3)(4) \cos \theta

1 = 9 + 16 + 24 \cos \theta

1 = 25 + 24 \cos \theta

24 \cos \theta = -24

\cos \theta = -1

\theta = 180^{}^{{}^{\circ}}

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