## Quick Reference

(of a plane)

Given a plane in 3-dimensional space, let **a** be the position vector of a point *A* in the plane, and **n** a normal vector to the plane. Then the plane consists of all points *P* whose position vector **p** satisfies (**p**−**a**). **n**=**0**. This is a vector equation of the plane. It may also be written **p**. **n**=constant. By supposing that **p** has components *x*, *y*, *z*, that **a** has components *x*_{1}, *y*_{1}, *z*_{1}, and that **n** has components *l*, *m*, *n*, the first form of the equation becomes *l*(*x*−*x*_{1})+*m*(*y*−*y*_{1})+*n*(*z*−*z*_{1})=0, and the second form becomes the standard linear equation *lx*+*my*+*nz*=constant.

*Subjects:*
Mathematics.

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