( 718, #71) If a, b and c are not all 0, show that the equation ax + b

( 718, #71) If a, b and c are not all 0, show that the equation ax + by + cz = d represents a plane and
< a, b, c > is a normal vector to the plane. Hint: Suppose and rewrite the equation in the form:
Solution:

ax + by + cz = d ax - d + by + cz = 0

This is the equation of a plane with the normal vector < a, b, c >. The same can be done
for , and the normal vector in both cases will also be < a, b, c >.

by: nl