Find the equation of the plane through the points (2,2,1) and (9,3,6) and perpendicular to the plane `2x+6y+6z=1`

Explanation

According to given questions , The Equation of any plane through (2,2,1) is `a(x-2)+b(y-2)+c(z-1)=0 - (1)`

therefore, it passes through (9,3,6)

therefore, a(9-2)+b(3-2)+c(6-1)=0

therefore, `7 a+b+5 c=0 cdots-(2)`

Also plane (1) is perpendicular to the plane.


` 2 x+6 y+6 z=9 `

therefore , a(2)+b(6)+c(6)=0
`(therefore a_{1} a_{2}+b_{1} b_{2}+c_{1} c_{2}=0`)

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