Question

Multiple choice: Can you please explain how to answer this?
Which point does not lie on the same plane as the points P(1,5,6), Q(-2,-3,4) and R(-1,3,2)

a) S(0,4,4)
b) S(4,13,8)
c) S(0,-1,8)
d) S(1,-3,2)

Answer 1

vector QP = 3 i + 8 j + 2 k
vector QR = 1 i + 6 j - 2 k

cross product
i j k
3 8 2
1 6 -2

-28 i + 8 j + 10 k
or
-14 i + 4 j + 5 k
so for plane
-14 x + 4 y + 5 z = d
try (1,5,6) to get d
-14 +20 + 30 = d
d = 36
check with (-1,3,2)
14 + 12 + 10 = 36 sure enough we are on a roll

NOW
put in (0,4,4)
0 + 4*4 + 5*4 = 16+20 = 36
so point (a) is in the plane
now do the other three points and see which one is not 36