Find the equation for the plane passing through the points P

Find the equation for the plane passing through the points P1=(4, 5, 2), P2=(0, 9, 6), and P3=(9, 8, 0)

P1=(4, 5, 2), P2=(0, 9, 6), and P3=(9, 8, 0)

vector P1P2 = ( 0 - (-4) , -9 - (-5) , -6 - (-2) ) = ( 4 , -4 , -4)

vector P1P3 = ( -9 -(-4) , -8 - (-5) , 0- (-2) ) = ( -5 , -3 , 2)

cross product of P1P2 and P1P3 = ( 4 , -4 , -4) x ( -5 , -3 , 2) = (-20 , 12, -32 )

Equation of plane : ax +by +cz +d =0

-20x +12y -32z +d =0

plug (-4, -5 , -2) to find d:

-20*(-4) +12(-5) -32(-2) +d =0

80-60 +64 +d =0

d= -84

So, Equation of plane : -20x +12y -32z -84 =0

-5x +3y -8z -21 =0