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Mathematics
Problem
Let
a
^
\hat{a}
a
^
,
b
^
\hat{b}
b
^
,
c
^
\hat{c}
c
^
are three unit vectors such that
a
^
+
b
^
+
c
^
\hat{a}+\hat{b}+\hat{c}
a
^
+
b
^
+
c
^
is also a unit vector. If pairwise angles between
a
^
\hat{a}
a
^
,
b
^
\hat{b}
b
^
;
c
^
\hat{c}
c
^
are
q
1
q_1
q
1
,
q
2
q_2
q
2
and
q
3
q_3
q
3
respectively then
cos
q
1
+
cos
q
2
+
cos
q
3
\cos q_1+\cos q_2+\cos q_3
cos
q
1
+
cos
q
2
+
cos
q
3
equals A. 3 B. -3 C. 1 D. -1
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