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Byju's Answer
Standard XII
Mathematics
Equation of a Plane Passing through Three Points
Find the vect...
Question
Find the vector and Cartesian equations of the plane passing through the points with position vectors
3
→
i
+
4
→
j
+
2
→
k
,
2
→
i
−
2
→
j
−
→
k
, and
7
→
i
+
→
j
+
→
k
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Solution
Equation f the perpendicular to the plane
→
n
=
∣
∣ ∣ ∣
∣
→
i
→
j
→
k
1
6
3
−
4
3
1
∣
∣ ∣ ∣
∣
=
−
3
→
i
−
13
→
j
+
27
→
k
Equation of plane passing through three given points is given by:
(
→
n
)
⋅
(
→
r
−
→
r
o
)
=
0
⇒
(
−
3
→
i
−
13
→
j
+
27
→
k
)
⋅
(
(
x
−
3
)
→
i
+
(
y
−
4
)
→
j
+
(
z
−
2
)
→
k
)
=
0
Cartesian form of plane :
=
−
3
(
x
−
3
)
−
13
(
y
−
4
)
+
27
(
z
−
2
)
=
0
=
−
3
x
−
13
y
+
27
z
+
7
=
0
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0
Similar questions
Q.
The vector equation of the plane through the point
→
i
+
2
→
j
−
→
k
and
⊥
to the line of intersection of the plane
→
r
.
(
3
→
i
−
→
j
+
→
k
)
=
1
and
→
r
.
(
→
i
+
4
→
j
−
2
→
k
)
=
2
is
Q.
Find the lengths of the following vectors :
3
→
i
+
2
→
j
−
→
k
,
√
2
i
−
√
3
k
,
5
→
i
+
4
→
j
−
2
→
k
Q.
Let
A
be vector parallel to line of intersection of planes
P
1
and
P
2
through origin.
P
1
is parallel to the vectors
2
→
j
+
3
→
k
and
4
→
j
−
3
→
k
and
P
2
is parallel to
→
j
−
→
k
and
3
→
i
+
3
→
j
, then the angle between
A
and
2
→
i
+
→
j
−
2
→
k
is
Q.
The unit vector which is orthogonal to the vector
→
a
=
3
→
i
+
2
→
j
+
6
→
k
and is coplanar with the vectors
→
b
=
2
→
i
+
→
j
+
→
k
and
→
c
=
→
i
−
→
j
+
→
k
is
Q.
Let
P
,
Q
,
R
be points with position vectors
→
r
1
=
3
→
i
−
2
→
j
−
→
k
,
→
r
2
=
→
i
+
3
→
j
+
4
→
k
and
→
r
3
=
2
→
i
+
→
j
−
2
→
k
relative to an origin
O
. The distance of
P
from the plane
O
Q
R
is (magnitude)
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