Question

Points A, B, and C are noncollinear. How many planes can be determined by A, B, and C?

Answer 1

In 3-dimensional space if the points A, B, and C are noncollinear, i.e. do not
belong to the same line,
then there exists a UNIQUE plane passing through
these points.

Therefore AB and AC are distinct lines.
Therefore by one
of axioms of elementary geometry, these lines determine a unique plane.