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Question
Write a vector normal to the plane \[\vec{r} = l \vec{b} + m \vec{c} .\]
Solution
\[\text{ The equation of the given plane is } \]
\[ \vec{r} = l \vec{b} + m \vec{c} \]
\[\text{ So, the plane passes parallel to the vectors } \vec{b} \text{ and } \vec{c} .\]
\[\text{ So, the vector normal to the plane is } \vec{b} \times \vec{c} .\]
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