Question

A and B are at an angle of 60° with each other. Their resultant makes an angle of 45° with a. If \( b = 2 \) units, then \( a \) is:

• A. \( \sqrt{3} \)
• B. \( \sqrt{3} + 1 \)
• C. \( \sqrt{2} \)
• D. \( \sqrt{3} - 1 \)

Hint:

When adding two vectors at an angle, use the law of cosines to find the magnitude of the resultant and solve for unknowns based on the given information.

Answer 1

The Correct Option is D

Using the law of cosines for the resultant of two vectors \( \vec{A} \) and \( \vec{B} \), we know the following relation: \[ R^2 = a^2 + b^2 + 2ab \cos \theta \] Given that the angle between \( a \) and \( b \) is \( 60^\circ \), we can substitute the values for \( b = 2 \) and solve for \( a \). After solving, we find: \[ a = \sqrt{3} - 1 \]
Thus, the correct answer is (d).