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Question

The points A(1,3,0),B(2,2,1) and C(1,1,3) determine a plane. The distance of the plane ABC from the point D(5,7,8) is

A
66
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B
71
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C
73
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D
76
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Solution

The correct option is A 66
Equation of plane passing through A(1,3,0),B(2,2,1),C(1,1,3) will have directionAB×BC=i7j4k
so plane x+7y+4z=c will contain C(1,1,3) so itwill satisfy plane'equation
1+7(1)+4(3)=c
c=20
hence equation of plane will be x+7y+4z=20
distance of (5,7,8) from the plane will be 1(5)+7(7)+4(8)2012+72+42=6666=66unit

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