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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

7

unit.

Options

A $120^{}^{{}^{\circ}}$
B $180^{}^{{}^{\circ}}$
C $90^{}^{{}^{\circ}}$
D $0^{}^{{}^{\circ}}$

Correct answer

D. $0^{}^{{}^{\circ}}$

Step-by-step solution

Let the two vectors be

\vec{A}

and

\vec{B}

with magnitudes

A = 3

and

B = 4

.

The magnitude of the resultant vector is given by

R = \sqrt{A^2 + B^2 + 2AB \cos \theta}

, where

\theta

is the angle between the vectors.

Given

R = 7

, squaring both sides gives:

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

7^2 = 3^2 + 4^2 + 2(3)(4) \cos \theta

49 = 9 + 16 + 24 \cos \theta

49 = 25 + 24 \cos \theta

24 = 24 \cos \theta

\cos \theta = 1

\theta = 0^{}^{{}^{\circ}}

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