1
You visited us
1
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
Write the dis...
Question
Write the distance of the plane
r
→
·
2
i
^
-
j
^
+
2
k
^
=
12
from the origin.
Open in App
Solution
The given equation of the plane is
r
→
.
2
i
^
-
j
^
+
2
k
^
=
12
or
r
→
.
n
→
=
-
6
,
where
n
→
=
2
i
^
-
j
^
+
2
k
^
n
→
=
4
+
1
+
4
=
3
For reducing the given equation to normal form, we need to divide both sides by
n
→
. Then, we get
r
→
.
n
→
n
→
=
12
n
→
⇒
r
→
.
2
i
^
-
j
^
+
2
k
^
3
=
12
3
⇒
r
→
.
2
3
i
^
-
1
3
j
^
+
2
3
k
^
=
4
.
.
.
1
The equation of the plane in normal form is
r
→
.
n
^
=
d
.
.
.
2
(where
d
is the distance of the plane from the origin)
Comparing (1) and (2),
length of the perpendicular from the origin to the plane =
d
= 4 units
Suggest Corrections
0
Similar questions
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
