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Manipal Entrance Test 2018 Math Paper
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© examsnet.com
Question : 2
Total: 70
A parallelogram is constructed on the vectors
→
a
=
3
α
−
β
,
→
b
=
α
+
3
β
.
If
|
α
|
=
|
β
|
=
2
and the angle between
α
and
β
is
π
3
,
then length of a diagonal of the parallelogram is
4
√
3
4
√
5
4
√
7
None of these
Validate
Solution:
Given,
→
a
=
3
α
−
β
,
→
b
=
α
+
3
β
and
|
α
|
=
|
β
|
=
2
|
→
a
+
→
b
|
2
=
|
4
→
α
+
2
→
β
|
2
=
16
|
→
α
|
2
+
4
|
β
|
2
+
16
|
→
α
|
|
→
β
|
cos
π
3
=
16
(
4
)
+
4
(
4
)
+
16
(
2
×
2
)
×
1
2
=
112
⇒
|
→
a
+
→
b
|
=
4
√
7
© examsnet.com
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