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Question

The direction ratios of the normal to the plane passing through the points (1,−2,3),(−1,2,−1) and parallel to the line x−22=y+13=z4 are proportional to.

A
2:3:4
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B
4:0:7
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C
2:0:1
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D
2:0:1
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Solution

The correct option is C 2:0:1
The equation of a plane passing through (1,2,3) is a(x1)+b(y+2)+c(z3)=0 ........(i)
It passes through (1,2,1) and is parallel to the given line.
a(2)+b(4)+c(4)=0
and 2a+3b+4c=0
a28=b0=c14
a2=b0=c1
Hence, a:b:c=2:0:1.

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