Question

Let \( \vec{a} \) and \( \vec{b} \) be two vectors such that \( |\vec{a}| = |\vec{b}| \) and \( |\vec{a}+2\vec{b}| = |2\vec{a}-\vec{b}| \). If \( \vec{c} \) is a vector parallel to \( \vec{a} \) then the angle between \( \vec{b} \) and \( \vec{c} \) is

• A. \( 0^\circ \)
• B. \( 30^\circ \)
• C. \( 60^\circ \)
• D. \( 90^\circ \)

Hint:

When an equation involves magnitudes of vector sums or differences, squaring both sides is a powerful technique. It converts the problem into dot products using the identity \( |\vec{v}|^2 = \vec{v} \cdot \vec{v} \), which often leads to a simple relationship between the vectors.

Answer 1

The Correct Option is D