alleryWhich non-parametric vector condition represents the line through points with position vectors $\bar a$ and $\bar b$?
A$(\bar r-\bar a)\times(\bar b-\bar a)=0$
B$(\bar r-\bar a)\cdot(\bar b-\bar a)=0$
C\(\bar r\cdot\bar a=\bar r\cdot\bar b\)
D$\bar r\times(\bar a+\bar b)=0$
Answer & Solution
Correct answer: A. $(\bar r-\bar a)\times(\bar b-\bar a)=0$
A point $\bar r$ lies on the line through $\bar a$ and $\bar b$ exactly when the vector $\bar r-\bar a$ is parallel to $\bar b-\bar a$.
Parallel vectors have zero cross product, so $(\bar r-\bar a)\times(\bar b-\bar a)=0$.
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