Provide an appropriate response.
-If $\mathrm{a}, \mathrm{b}$, and $\mathrm{c}$ are all nonzero, then determine if the plane $\mathrm{ax}+\mathrm{by}+\mathrm{cz}=1$ always intersects all three coord inate planes (i.e. the planes $x=0, y=0, z=0$ ), sometimes intersects them, or never intersects them.
A)A lways
B) Sometimes
C) Never

Question

Quizplus · Accepted Answer

The plane $ax + by + cz = 1$ will always intersect the coordinate planes $x=0$, $y=0$, and $z=0$ as long as $a$, $b$, and $c$ are nonzero, because setting any two variables to zero will yield a nonzero solution for the third variable.

Provide an Appropriate Response a,b\mathrm{a}, \mathrm{b}a,b , And c\mathrm{c}c Are All Nonzero, Then Determine If the Plane

Provide an Appropriate Response $\mathrm{a}, \mathrm{b}$ , And $\mathrm{c}$ Are All Nonzero, Then Determine If the Plane