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A plane passes through the point (1, 1...

A plane passes through the point (1, 1, 1). If b, c, a are the direction ratios of a normal to the plane where a, b, c` (altbltc)` are the prime factors of 2001, then the equation of the plane II is

A

`29x+31y+z=63`

B

`23x+29y-29z=23`

C

`23x+29y+3z=55`

D

`31x+37y+3z=71`

Text Solution

Verified by Experts

The correct Answer is:
C
The equation of the plane is
`b(x-1)+c(y-1)+a(z-1)=0`……………i
Now, `2001=3xx23xx29`
`:.altbltcimpliesa=3,b=23` and `c=29`
Subsituting the values a,b,c in i we obtain
`23x+29y+3z=55` as the equation of the required plane.
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