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Mathematics
Mathematics
Problem
Let the vectors
P
Q
\boldsymbol{PQ}
PQ
,
O
R
\boldsymbol{OR}
OR
,
R
S
\boldsymbol{RS}
RS
,
S
T
\boldsymbol{ST}
ST
,
T
U
\boldsymbol{TU}
TU
and
U
P
\boldsymbol{UP}
UP
represent the sides of a regular hexagon.
Statement I
P
Q
×
(
R
S
+
S
T
)
≠
0
\boldsymbol{PQ} \times (\boldsymbol{RS} + \boldsymbol{ST}) \neq 0
PQ
×
(
RS
+
ST
)
=
0
Statement II
P
Q
×
R
S
=
0
\boldsymbol{PQ} \times \boldsymbol{RS} = 0
PQ
×
RS
=
0
and
P
Q
×
S
T
≠
0
\boldsymbol{PQ} \times \boldsymbol{ST} \neq 0
PQ
×
ST
=
0
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