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Mathematics
Mathematics
Problem
Let
O
O
O
be the origin and
O
X
,
O
Y
,
O
Z
OX, OY, OZ
O
X
,
O
Y
,
O
Z
be three unit vectors in the directions of the sides,
Q
R
,
R
P
,
P
Q
QR, RP, PQ
QR
,
R
P
,
P
Q
respectively of a
Δ
P
Q
R
\Delta PQR
Δ
P
QR
.
∣
O
X
⃗
×
O
Y
⃗
∣
=
|\vec{OX} \times \vec{OY}| =
∣
O
X
×
O
Y
∣
=
a.
sin
(
P
+
Q
)
\sin(P+Q)
sin
(
P
+
Q
)
b.
sin
(
P
+
R
)
\sin(P+R)
sin
(
P
+
R
)
c.
sin
(
Q
+
R
)
\sin(Q+R)
sin
(
Q
+
R
)
d.
sin
2
R
\sin 2R
sin
2
R
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