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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
. If the triangle
P
Q
R
PQR
P
QR
varies, then the minimum value of
cos
(
P
+
Q
)
+
cos
(
Q
+
R
)
+
cos
(
R
+
P
)
\cos(P+Q) + \cos(Q+R) + \cos(R+P)
cos
(
P
+
Q
)
+
cos
(
Q
+
R
)
+
cos
(
R
+
P
)
is a.
−
3
2
-\frac{3}{2}
−
2
3
b.
3
2
\frac{3}{2}
2
3
c.
5
3
\frac{5}{3}
3
5
d.
−
5
3
-\frac{5}{3}
−
3
5
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