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Question

The direction ratios of a normal to the plane passing through (1, 0, 0), (0, 1, 0) and making an angle π4 with the plane x + y = 3 are :

A
(1,2,1)
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B
(1,12)
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C
(1,1,2)
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D
(2,1,1)
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Solution

The correct option is B (1,12)
Any plane through (1, 0, 0), (0, 1, 0) can be taken as
x1+y1+zc=1

D.R.’s of normal to this plane are 1, 1, 1c
This plane is inclined at an angle π4 with the plane x + y = 3
cos(π4)=1+1+0.1c12+12+1c21+14c1(2c2+1)2=12
12 i.e., c =±12
D.R.’s of normal of the required plane are (1,1,2) or (1,12)

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