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Byju's Answer
Standard XII
Mathematics
Equation of a Plane : Vector Form
The Cartesian...
Question
The Cartesian equation of a line is:
2
x
−
3
=
3
y
+
1
=
5
−
6
z
. Find the vector equation of a line passing through
(
7
,
−
5
,
0
)
and parallel to the given line.
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Solution
Given line is
L
:
x
−
3
/
2
1
/
2
=
y
+
1
/
3
1
/
3
=
z
−
5
/
6
−
1
/
6
That means
→
v
=
(
1
/
2
,
1
/
3
,
−
1
/
6
)
∴
Vector equation of a line passing through
→
r
0
=
P
0
(
7
,
−
5
,
0
)
and parallel to
L
(
Means parallel to vector
→
v
)
→
L
1
:
→
r
=
→
r
0
+
λ
→
v
→
r
=
(
7
,
−
5
,
0
)
+
λ
(
1
/
2
,
1
/
3
,
−
1
/
6
)
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