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Question

The direction ratios of normal to the plane through the points (0,1,0) and (0,0,1) and making an angle π4 with the plane yz+5=0 are :

A
2,1,1
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B
23,1,1
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C
2,1,1
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D
2,2,2
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Solution

The correct option is A 2,1,1
BONUS QUESTION : Two options are correct.

Direction of ratios of line through A(0,1,0) and B(0,0,1) is (0,1,1)
Let DR's of normal to plane be (a,b,c)
b+c=0
cosπ4=a(0)+b(1)+c(1)a2+b2+c2(1)2+(1)2
12=bca2+b2+c2×2
a2+b2+c2=b2+c22bc
a2=2bc
a2=2b(b)
a2=2b2
a=2b
DR's of normal to plane are (2,1,1) or (2,1,1) or any multiple of it.
So, (2,2,2) is also correct.

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