alleryWhich non-parametric vector equation represents the line passing through the point with position vector $\bar a$ and parallel to $\bar b$?
A$\bar r\times \bar b=\bar a\times \bar b$
B$\bar r\cdot \bar b=\bar a\cdot \bar b$
C$(\bar r-\bar a)\cdot \bar b=0$
D$\bar r=\bar a\times \bar b$
Answer & Solution
Correct answer: A. $\bar r\times \bar b=\bar a\times \bar b$
If a point with position vector $\bar r$ lies on the line through $\bar a$ parallel to $\bar b$
then $\bar r-\bar a$ is parallel to $\bar b$.
**Therefore $(\bar r-\bar a)\times \bar b=0$, which is equivalent to $\bar r\times\bar b=\bar a\times\bar b$.**
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