If three points $A(\vec a), B(\vec b), C(\vec c)$ are **collinear**, then $\overrightarrow{AC}$ must equal:
A$\overrightarrow{AB} \times \overrightarrow{BC}$
BSome scalar multiple of $\overrightarrow{AB}$
C$\overrightarrow{AB} + \overrightarrow{BC}$ which is the zero vector
D$\overrightarrow{0}$ always
Answer & Solution
Correct answer: B. Some scalar multiple of $\overrightarrow{AB}$
Three points are collinear iff the vectors along the line are parallel. So $\overrightarrow{AC} = k\,\overrightarrow{AB}$ for some scalar $k$. Option C is partly true geometrically but the sum isn't the zero vector unless A = C.
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