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Byju's Answer
Standard XII
Mathematics
Equation of a Plane Passing through a Point and Perpendicular to a Given Vector
The vector eq...
Question
The vector equation of a plane which is at a distance of 9 units f
r
o
m
t
h
e
o
r
i
g
i
n
a
n
d
w
h
i
c
h
i
s
n
o
r
m
a
l
t
o
t
h
e
v
e
c
t
o
r
2
ˆ
i
−
ˆ
j
+
2
ˆ
k
is
A
→
r
.
(
2
ˆ
i
−
ˆ
j
+
2
ˆ
k
)
=
27
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B
→
r
.
(
2
ˆ
i
−
ˆ
j
+
2
ˆ
k
)
=
9
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C
→
r
.
(
2
ˆ
i
−
ˆ
j
+
2
ˆ
k
)
=
3
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Solution
The correct option is
A
→
r
.
(
2
ˆ
i
−
ˆ
j
+
2
ˆ
k
)
=
27
The vector equation of a plane is given in the form
→
r
.
ˆ
n
=
d
Here d = 9 and
ˆ
n
=
2
ˆ
i
−
ˆ
j
+
2
ˆ
k
√
2
2
+
(
−
1
)
2
+
2
2
=
2
3
ˆ
i
−
1
3
ˆ
j
+
2
3
ˆ
k
So,
−
→
r
.
(
2
3
ˆ
i
−
1
3
ˆ
j
+
2
3
ˆ
k
)
=
9
→
r
.
(
2
ˆ
i
−
ˆ
j
+
2
ˆ
k
)
=
27
.
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Similar questions
Q.
Find the vector equation of plane which is at a distance of
8
units from the origin and which is normal to the vector
2
i
+
j
+
2
k
.
Q.
The vector equation of a plane which is at a distance of 9 units f
r
o
m
t
h
e
o
r
i
g
i
n
a
n
d
w
h
i
c
h
i
s
n
o
r
m
a
l
t
o
t
h
e
v
e
c
t
o
r
2
ˆ
i
−
ˆ
j
+
2
ˆ
k
is