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Byju's Answer
Standard XII
Mathematics
Equation of a Plane : Normal Form
The direction...
Question
The direction ratios of a normal to the plane passing through
(
0
,
1
,
1
)
,
(
1
,
1
,
2
)
and
(
−
1
,
2
,
−
2
)
are
A
(
1
,
1
,
1
)
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B
(
2
,
1
,
−
1
)
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C
(
1
,
2
,
−
1
)
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D
(
1
,
−
2
,
−
1
)
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Solution
The correct option is
B
(
1
,
1
,
1
)
The
3
given points are
A
(
0
,
0
,
1
)
,
B
(
0
,
1
,
2
)
and
C
(
1
,
2
,
3
)
The dr's of
A
B
are
(
0
,
1
,
1
)
The dr's of
B
C
are
(
1
,
1
,
1
)
The normal to the plane will be perpendicular to both these lines.
Hence,
n
=
A
B
×
B
C
n
=
(
0
,
1
,
−
1
)
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0
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