2
You visited us
2
times! Enjoying our articles?
Unlock Full Access!
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
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
→
r
.
(
2
ˆ
i
−
ˆ
j
+
2
ˆ
k
)
=
9
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
→
r
.
(
2
ˆ
i
−
ˆ
j
+
2
ˆ
k
)
=
3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
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
.
Suggest Corrections
0
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