Collinear vectors are vectors that lie on the same straight line, meaning they have the same or exact opposite direction. When vectors are collinear, there exists a scalar factor that can multiply one vector to turn it into the other. This is a key concept for identifying the orientation of vectors in terms of parallel alignment.
- Vectors \( \overrightarrow{\mathbf{A}} \) and \( \overrightarrow{\mathbf{B}} \) are collinear if there exists a scalar \( k \) such that \( \overrightarrow{\mathbf{A}} = k \cdot \overrightarrow{\mathbf{B}} \).
- If \( k > 0 \), the vectors point in the same direction.
- If \( k < 0 \), the vectors point in opposite directions.
In scenarios like the given exercise, where the magnitudes satisfy \( A + B = C \) and the vector sum aligns perfectly, this implies that \( \overrightarrow{\mathbf{A}} \) and \( \overrightarrow{\mathbf{B}} \) are not only collinear but also in the same direction, further indicating that the sum of the vectors extends to form a straight line.