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JEE Main Math Class 12 Vector Algebra Part 1 Questions
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© examsnet.com
Question : 25
Total: 100
If
→
a
and
→
b
are non-collinear vectors, then the value of
α
for which the vectors
→
u
=
(
α
−
2
)
→
a
+
→
b
and
→
v
=
(
2
+
3
α
)
→
a
−
3
→
b
are collinear is:
[Online April 23, 2013]
3
2
2
3
−
3
2
−
2
3
Validate
Solution:
Since,
→
u
and
→
v
are collinear, therefore
→
k
u
+
→
v
=
0
⇒
[
k
(
α
−
2
)
+
2
+
3
α
]
→
a
+
(
k
−
3
)
→
b
=
0
.......(i)
Since
→
a
and
→
b
are non-collinear, then for some constant
m
and
n
,
m
→
a
+
n
→
b
=
0
⇒
m
=
0
,
n
=
0
Hence from equation (i)
k
−
3
=
0
⇒
k
=
3
And
k
(
α
−
2
)
+
2
+
3
α
=
0
⇒
3
(
α
−
2
)
+
2
+
3
α
=
0
⇒
α
=
2
3
© examsnet.com
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