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The equation of plane containing the line x+13=y22=z+21 and the point (0,7,7) is

A
x+y+z=1
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B
x+y+z=2
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C
x+y+z=0
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D
None of the above
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Solution

The correct option is B x+y+z=0
The equation of the plane containing the line
x+13=y32=z+21 is
a(x+1)+b(y3)+c(z+2)=0.....(i)
where, 3a+2b+c=0.....(ii)
This passes through (0,7,7)
a+4b5c=0....(iii)
From Eqs. (ii) and (iii), we get
a14=b14=c14 or a1=b1=c1
So, the required plane is x+y+z=0.

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