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Byju's Answer
Standard X
Mathematics
Equation of a Line Parallel to a Straight Line
Find the equa...
Question
Find the equation of the plane through the line x+1/-3 = y-3/2 = z+2/1 and the point (0,7,-7). Show also that the line x= 7-y/3 = z+7/2 lies on this plane
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Solution
Dear student,
We
know
that
equation
of
a
plane
passing
through
the
point
x
1
,
y
1
,
z
1
and
having
direction
ratios
of
the
normal
to
the
plane
as
a
,
b
,
c
is
a
x
-
x
1
+
b
y
-
y
1
+
c
z
-
z
1
=
0
Now
,
equation
of
the
plane
passing
through
0
,
7
,
-
7
and
having
direction
ratios
of
the
normal
to
the
plane
as
a
,
b
,
c
is
a
x
-
0
+
b
y
-
7
+
c
z
+
7
=
0
.
.
.
.
.
.
.
.
1
Now
,
the
given
equation
of
the
line
is
x
+
1
-
3
=
y
-
3
2
=
z
+
2
1
.
.
.
.
.
.
2
Now
,
the
line
2
passes
through
-
1
,
3
,
-
2
and
having
direction
ratios
-
3
,
2
,
1
.
Since
the
plane
1
contains
the
line
2
,
then
plane
1
must
pass
through
-
1
,
3
,
-
2
.
Now
,
from
1
,
we
get
a
-
1
-
0
+
b
3
-
7
+
c
-
2
+
7
=
0
⇒
-
a
-
4
b
+
5
c
=
0
⇒
a
+
4
b
-
5
c
=
0
.
.
.
.
.
.
.
3
Since
plane
1
contains
the
line
2
,
line
is
parallel
to
the
plane
.
Now
,
-
3
a
+
2
b
+
c
=
0
.
.
.
.
.
.
.
.
.
4
Solving
3
and
4
by
cross
multiplication
,
a
4
+
10
=
b
15
-
1
=
c
2
+
12
Let
a
14
=
b
114
=
c
14
=
k
⇒
a
=
b
=
c
=
k
Now
,
from
1
,
we
get
k
x
-
0
+
k
y
-
7
+
k
z
+
7
=
0
⇒
x
+
y
+
z
=
0
Regards
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0
Similar questions
Q.
Find the equation of the plane containing the line
x
+
1
-
3
=
y
-
3
2
=
z
+
2
1
and the point (0, 7, −7) and show that the line
x
1
=
y
-
7
-
3
=
z
+
7
2
also lies in the same plane.
Q.
Find the equation of the plane containing line
x
+
1
−
3
=
y
−
3
2
=
z
+
2
1
and point
(
0
,
7
,
−
7
)
.
Q.
An equation of the plane containing the line
x
+
1
3
=
y
−
3
2
=
z
+
2
1
and the point
(0, 7, -7) is
Q.
The equation of the plane containing the line
x
+
1
−
3
=
y
−
3
2
=
z
+
2
1
and passing through the point
(
0
,
7
,
−
7
)
is
Q.
The equation of the plane through the line x + y + z + 3 = 0 = 2x − y + 3z + 1 and parallel to the line
x
1
=
y
2
=
z
3
is
(a) x − 5y + 3z = 7
(b) x − 5y + 3z = −7
(c) x + 5y + 3z = 7
(d) x + 5y + 3z = −7
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