Question

Two vectors of same magnitude have a resultant equal to either of the two vectors. The angle between two vectors is

• A. \( \cos^{-1}(-0.3) \)
• B. \( \cos^{-1}(-0.6) \)
• C. \( \cos^{-1}(-0.4) \)
• D. \( \cos^{-1}(-0.5) \)

Hint:

For two vectors of the same magnitude, the angle between them can be determined using the formula for the magnitude of the resultant vector.

Answer 1

The Correct Option is D

Step 1: Magnitude of the resultant.
The magnitude of the resultant of two vectors \( \mathbf{A} \) and \( \mathbf{B} \) with the same magnitude is given by: \[ R = \sqrt{A^2 + B^2 + 2AB \cos \theta} \] For the resultant to be equal to either of the two vectors, the angle \( \theta \) between the vectors must satisfy \( \cos \theta = -0.5 \).
Step 2: Conclusion.
Thus, the correct answer is (D) \( \cos^{-1}(-0.5) \).