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Byju's Answer
Standard XII
Mathematics
Condition of Concurrency of 3 Straight Lines
Q.10. Find th...
Question
Q.10. Find the vector equation of the plane passing through the points (1, 1, 1), (1, - 1, 1) and (- 7, - 3, - 5).
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Solution
Dear student
Let
the
points
be
A
(
1
,
1
,
1
)
,
B
(
1
,
-
1
,
1
)
,
C
(
-
7
,
-
3
-
,
5
)
The
required
plane
passes
through
the
point
A
(
1
,
1
,
1
)
whose
position
vector
is
a
→
=
i
^
+
j
^
+
k
^
and
is
normal
to
the
vector
n
→
given
by
n
→
=
AB
→
×
AC
→
We
have
,
AB
→
=
i
^
-
j
^
+
k
^
-
(
i
^
+
j
^
+
k
^
)
=
-
2
j
^
and
AC
→
=
(
-
7
i
^
-
3
j
^
-
5
k
^
)
-
(
i
^
+
j
^
+
k
^
)
=
-
8
i
^
-
j
^
-
6
k
^
∴
n
→
=
AB
→
×
AC
→
=
i
^
j
^
k
^
0
-
2
0
-
8
-
1
-
6
=
i
^
12
-
j
^
(
0
)
+
k
^
(
-
16
)
=
12
i
^
-
16
k
^
The
vector
equation
of
the
required
plane
is
r
→
.
n
→
=
a
→
.
n
→
⇒
r
→
.
12
i
^
-
16
k
^
=
(
i
^
+
j
^
+
k
^
)
.
(
12
i
^
-
16
k
^
)
⇒
r
→
.
12
i
^
-
16
k
^
=
12
-
16
⇒
r
→
.
(
3
i
^
-
4
j
^
)
+
1
=
0
Regards
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Q.
Find the vector equation of the plane passing through the points (1, 1, 1), (1, −1, 1) and (−7, −3, −5).
