If P(1, 0, - 3) is the foot of the perpendicular from the origin to the plane, then the cartesian equation of the plane is _____________ .

 

 

Answers (1)

Assume diction cosine of the normal (a,b,c)

Equation of plane passing through (x_{1},y_{1},z_{1}) 

a\left(x-x_{1}\right)+b\left(y-y_{1}\right)+c\left(z-z_{1}\right)=0

Point P(1,0,-3)

a(x-1)+b(y-0)+c(z-(-3))=0

\\\ \text { Direction cosine of normal } \\ (a,b,c) \equiv (1-0,0-0,-3-0) \\ (a,b,c) \equiv (1,0,-3) \\

Equation of the plane 

\\ 1(x-1)+0(y-0)-3(z-(-3))=0 \\ x -3z = 10

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