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Question

Direction ratios of the normal to the plane which passes through the point (1,0,0) and (0,1,0) and makes an angle π4 with the plane x+y=3 are

A
(1,1,2)
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B
(1,1,12)
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C
(1,1,12)
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D
(1,1,0)
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Solution

The correct option is A (1,1,2)
The plane's equation in the intercept form is
x1+y1+zc=1
So, direction ratios of the normal are (1,1,1c) and that of the given plane are (1,1,0)
cosπ4=11+11+1c01+11/c2+1+1
12=221/c2+1+1
1c2+2=4c=±12

Therefore, direction ratios of the normal to the plane is (1,1,±2)

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