Question

The resultant of two vectors \( \mathbf{A} \) and \( \mathbf{B} \) is perpendicular to vector \( \mathbf{A} \), and the resultant magnitude is equal to half of the magnitude of \( \mathbf{B} \). The angle between \( \mathbf{A} \) and \( \mathbf{B} \) is:

• A. \( 30^\circ \)
• B. \( 60^\circ \)
• C. \( 150^\circ \)
• D. \( 120^\circ \)

Hint:

When two vectors are perpendicular, the angle between them can be derived using the resultant magnitude and properties of vector addition.

Answer 1

The Correct Option is C

When two vectors are perpendicular and their resultant is half of one vector's magnitude, we can use the law of cosines or vector addition properties to determine the angle between them. After solving the equations, we find that the angle between \( \mathbf{A} \) and \( \mathbf{B} \) is \( 150^\circ \). Thus, the correct answer is option (3).