Q. 224.2( 5 Votes )

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Answer :

We will solve this question by using planes method, first we will find the general equation of the plane containing all these points starting with the first point A,

a(x - 3) + b(y - 2) + c(z - 1) = 0


Now putting point C,


a(4 - 3) + b(2 - 2) + c( - 2 - 1) = 0


a + 0b – 3c = 0


Now putting point D,


a(6 - 3) + b(5 - 2) + c( - 1 - 1) = 0


3a + 3b - 2c = 0


Solving these equations by cross - multiplication method, we get,





a = 9λ, b = - 7λ, c = 3λ


The equation of the plane is,


9(x - 3) - 7(y - 2) + 3(z - 1) = 0


Putting point B in the equation,


9(4 - 3) - 7(x - 2) + 3(5 - 1) = 0


9 – 7x + 14 + 12 = 0


x = 5


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