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KEAM 2010 Math Paper
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© examsnet.com
Question : 13 of 120
Marks:
+1
,
-0
If the plane
3
x
+
y
+
2
z
+
6
=
0
is parallel to the line
3
x
−
1
2
b
=
3
−
y
=
z
−
1
a
,
then the value of
3
a
+
3
b
is
1
2
3
2
3
4
5
2
Validate
Solution:
Comparing the given equation of plane
3
x
+
y
+
2
z
+
6
=
0
with
l
x
+
m
y
+
n
z
+
d
=
0
⇒
l
=
3
,
m
=
1
,
n
=
2
Also, comparing given equation of line
x
−
1
3
2
b
3
=
3
−
y
=
z
−
1
a
with
x
−
x
1
a
1
=
y
−
y
1
b
1
=
z
−
z
1
c
1
,
we get
a
1
=
2
b
3
,
b
1
=
−
1
,
c
1
=
a
For parallel line
l
a
1
+
m
b
1
+
n
c
1
=
0
⇒
3
⋅
2
b
3
+
1
⋅
(
−
1
)
+
2
a
=
0
⇒
2
a
+
2
b
=
1
⇒
a
+
b
=
1
2
⇒
3
a
+
3
b
=
3
2
© examsnet.com
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