1.

A plane passes through the points (1, 1, 1). If b, c, a are the direction ratios of a normal to the plane where a, b, c (a lt b lt c) are the prime factors of 2001, then the equation of the plane is:

Answer»

`29x + 31y + 3z = 63`
`23x + 29Y – 29z = 23`
`23x + 29y + 3z = 55`
`31x + 37Y + 3z = 71`

Solution :The equation of the plane is
`b(x-1)+c(y-1)+a(z-1)=0`
Now, `2001=3xx23xx29`
`THEREFORE a lt b ltc rArr a = 3, b=23 and c=29`
Substituting the VALUES of a, b, c in (i), we obtain
`23x+26y+3z=55` as the equation of the required plane.


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