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Byju's Answer
Standard XII
Mathematics
Solution of Triangle
If P is a 3 ×...
Question
If P is a
3
×
3
orthogonal matrix
α
,
β
,
γ
are the angles made by a straight line OX, OY, OZ and
A
=
⎡
⎢
⎣
s
i
n
2
α
s
i
n
α
s
i
n
β
s
i
n
α
s
i
n
γ
s
i
n
α
s
i
n
β
s
i
n
2
β
s
i
n
β
s
i
n
γ
s
i
n
α
s
i
n
γ
s
i
n
β
s
i
n
γ
s
i
n
2
γ
⎤
⎥
⎦
&
Q
=
P
T
A
P
.
If
P
Q
6
P
T
=
K
A
then k is
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Solution
c
o
s
2
α
+
c
o
s
2
β
+
c
o
s
2
γ
=
1
⇒
s
i
n
2
α
+
s
i
n
2
β
+
s
i
n
2
γ
=
2
hence
A
2
=
2
A
⇒
A
3
=
2
2
A
⇒
A
6
=
2
5
A
A
2
=
Q
=
P
T
A
P
.
P
T
A
T
P
P
.
P
T
=
I
therefore
A
2
=
P
T
A
2
P
Similarly
Q
6
=
P
T
A
6
P
So
P
Q
6
P
T
=
P
(
P
T
A
6
P
)
P
T
=
A
6
=
32
A
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