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Byju's Answer
Standard XII
Mathematics
Product of Trigonometric Ratios in Terms of Their Sum
If |a×b|2 +...
Question
If
|
→
a
×
→
b
|
2
+
(
→
a
⋅
→
b
)
2
=
144
and
|
→
a
|
=
4
, then
|
→
b
|
=
A
16
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B
8
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C
3
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D
12
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Solution
The correct option is
C
3
Using the definition of cross and dot products
|
→
a
|
2
|
→
b
|
2
sin
2
θ
+
|
→
a
|
2
|
→
b
|
2
cos
2
θ
=
144
⇒
|
→
a
|
2
|
→
b
|
2
(
sin
2
θ
+
cos
2
θ
)
=
144
⇒
4
2
|
→
b
|
2
(
1
)
=
144
⇒
|
→
b
|
2
=
144
16
=
9
∴
|
→
b
|
=
3
Note:
|
→
a
×
→
b
|
=
|
→
a
|
→
b
|
sin
θ
and
→
a
⋅
→
b
=
|
→
a
|
|
→
b
|
cos
θ
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0
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