Question

how to prove 4 points coplaner in vector
ex prove for following
p(-1,4,3) q(3,2,5) r(-3,8,5) & s (-3,2,1)

Answer 1

take three vectors as
x=q-p
y=r-p
z=s-p
now if the scalar triple product of x, y, z ie., x.(yxz) = 0,
the four points are coplanar

Answer 2

4 points are co-planar if they lie on the same plane
note taht a plane is formed only when 2 axis intersect each other
if u know 3-d geometry visualise and do
in vector notation as i said before
u will get some (3,4,1) or 3i+4j+1k

if a point is lying on a particular plane then it should have only 2 co-ordinates
if it has 3 co-rdiantes then it is said to lie in space(suspended)
visualise