Question

If $\vec{c} = 5\vec{a} + 6\vec{b}$ and $3\vec{c} = \vec{a} - 4\vec{b}$ then}

• A. $\vec{a}, \vec{b}, \vec{c}$ are non-collinear
• B. $\vec{a}, \vec{b}, \vec{c}$ are in the same direction
• C. $\vec{a}, \vec{c}$ are in the same direction but $\vec{a}, \vec{b}$ are in the opposite direction
• D. $\vec{c}, \vec{b}$ are in the opposite direction and $\vec{a}, \vec{b}$ are in the same direction

Hint:

$\vec{u} = k\vec{v}$ means same direction if $k > 0$, opposite if $k < 0$.

Answer 1

The Correct Option is C