Find the vector equation of the plane passing through the points `A(2,2,-1),B(3,4,1)a n dC(7,0,6)dot` Also, find the Cartesian equation of the plane.

Explanation

The general equation of a plane through `(2,2−1)`
is
`a(x−2+b(y−2)+c(z+1)=0 ...(1)`

It will pass through `B(3,4,2) ` and `C(7,0,6)`
if
`a(3−2)+b(4−2)+c(2+1)=0⇒a+2b+3c=0 ...(2)`

and
`a(7−2)+b(0−2)+c(6+1)=0
⇒5a−2b+7c=0 ...(3)`

Solving (2) and (3) by cross-multiplication, we have

`a/(14+6)​=b/(15−7)​=c/(−2−10)​`

`⇒5a​=2b​=−3c​=(lambda)`

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