Find an equation of the plane. The plane through the points (2, 1, 2), (3, −8, 6), and (−2, −3, 1)

arenceabigns 2021-05-31 Answered
Find an equation of the plane. The plane through the points (2, 1, 2), (3, −8, 6), and (−2, −3, 1)
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Expert Answer

delilnaT
Answered 2021-06-01 Author has 94 answers

Let the given points be P(2,1,2),Q(3,-8,6), and R(-2,-3,1)
PQ=32,81,62=1,9,4
PR=22,31,12=4,4,1
PQ×PR=|ijk194441|=(9+16)i+(16+1)j+(436)k
=25i15j40k
Therefore, the normal vector to the plane is
n=25,15,40
Since, the plane passes through all the three points we can choose any point to find its equation. So, the equation of the plane through the point P(2,1,2) with normal vector n=25,15,40 is
25(x2)15(y1)40(z2)=0
25x5015y+1540z+80=0
25x15y40z+45=0

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