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UPSC NDA Math Model Paper 4
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© examsnet.com
Question : 54
Total: 120
If
|
→
a
|
=
3
,
|
→
b
|
=
4
and
|
→
a
×
→
b
|
=
6
, then find the value of
→
a
.
→
b
4
√
3
6
6
√
3
12
Validate
Solution:
Given:
|
→
a
|
=
3
,
|
→
b
|
=
4
and
|
→
a
×
→
b
|
=
6
As we know,
→
a
×
→
b
=
|
→
a
|
×
|
→
b
|
×
sin
θ
×
^
n
|
→
a
×
→
b
|
=
|
→
a
|
×
|
→
b
|
×
|
sin
θ
|
×
|
^
n
|
=
|
→
a
|
×
|
+
→
b
|
×
sin
θ
(∵ Magnitude of a unit vector is one)
⇒
sin
θ
=
|
→
a
×
→
b
|
|
→
a
|
×
|
→
b
|
=
6
12
=
1
2
∴
θ
=
30
°
Now,
cos
θ
=
cos
30
=
√
3
2
As we know that, If
→
a
and
→
b
are two vectors, then the scalar product between the given by:
→
a
.
→
b
=
|
→
a
|
×
|
→
b
|
×
cos
θ
∴
→
a
.
→
b
=
3
×
4
×
√
3
2
=
6
√
3
© examsnet.com
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