Question

Let \( \vec{a}, \vec{b}, \vec{c} \) be any three non-coplanar vectors. If \( m, n \) are scalars such that \( \vec{a} + \vec{b} = m\vec{c} \) and \( \vec{b} + \vec{c} = n\vec{a} \), then \( 3\vec{a} + 2\vec{b} + 2\vec{c} = \):

• A. \( \vec{a} - \vec{d} \)
• B. \( \vec{a} + \vec{d} \)
• C. 0
• D. \( \vec{b} + \vec{c} + 2\vec{d} \)

Hint:

For vector equations, use properties of linearity and the relationships between the vectors to simplify the equation.

Answer 1

The Correct Option is C

By using the given vector relations and applying vector operations, we can find that \( 3\vec{a} + 2\vec{b} + 2\vec{c} = 0 \).