1.

Find the equation of the plane through the points `A(2,2,-1),B(3,4,2)a n dC(7,0,6.)`A. `5x+2y+3z=17`B. `5x+2y-3z=17`C. `5x-2y+3z=17`D. none of these

Answer» Correct Answer - B
The general equation of a plane passing through (2,2,-1) is
`a(x-2)+b(y-2)+c(z+1)=0`………………i
It will pass through `B(3,4,2)` and `C(7,0,6)`, if
`a+2b+3c=0` ……………….ii
and `5a-2b+7c=0`…………….iii
Solving ii and iii by cross multiplication we have
`a/(14+6)=b/(15-7)=c/(-2-10)`
`impliesa/5=b/2=c/(-3)=lamda` (say)
`impliesa=5lamda, b=2lamda` and `c=-3lamda`
Substituting the values of a,b, and c in i we get
`5lamda(x-2)+2lamda(y-2)-3lamda(z+1)=0`
`implies5(x-2)+2(y-2)-3(z+1)=0`
`implies5x+2y-3z=17` which is the required equation of the plane.


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