Question

How many non collinear points are always co-planer?

Answer 1

Hint: We have to answer how many collinear points are always co-planer which means we have to check how many noncollinear points will always be in the same plane. We know that 2 different points can make a line.

Complete step by step answer:
We know that we can write the equation of any plane as $ ax+by+cz=d $ where a, b, c are variables and d is any constant
If we have certain point on this plane then the point (x, y, z) will satisfy the equation $ ax+by+cz=d $
If we are given one point $ \left( {{x}_{1}},{{y}_{1}},{{z}_{1}} \right) $
Then $ a{{x}_{1}}+b{{y}_{1}}+c{{z}_{1}}=d $ we can see there is one equation and 3 variables so there will be infinite possible plane that passes through $ \left( {{x}_{1}},{{y}_{1}},{{z}_{1}} \right) $
Similarly, if there is 2 points given there will be 2 equations and 3 unknowns so there will be an infinite number of solutions
If there is 3 given noncollinear point then there is 3 unknowns and 3 equation so there is only one solution possible and all the 3 points will make a unique plane
So 3 noncollinear points are always coplanar.

Note:
if 4 points are given they may not be on the same plane. It is similar to there may not exist any solution for 4 equation and 3 unknowns. If 3 collinear points are given then there are infinite numbers of planes that will pass through these 3 points.