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Mathematics
Mathematics
Problem
The angles of a triangle, two of whose sides are represented by vectors
3
(
a
^
×
b
^
)
\sqrt{3}(\hat{\boldsymbol{a}} \times \hat{\boldsymbol{b}})
3
(
a
^
×
b
^
)
and
b
^
−
(
a
⋅
b
^
)
a
^
\hat{\boldsymbol{b}} - (\boldsymbol{a} \cdot \hat{\boldsymbol{b}})\hat{\boldsymbol{a}}
b
^
−
(
a
⋅
b
^
)
a
^
, where
b
^
\hat{\boldsymbol{b}}
b
^
is a non-zero vector and
a
^
\hat{\boldsymbol{a}}
a
^
is a unit vector in the direction of
a
\boldsymbol{a}
a
, are a.
tan
−
1
(
3
)
\tan^{-1}(\sqrt{3})
tan
−
1
(
3
)
b.
tan
−
1
(
1
/
3
)
\tan^{-1}(1/\sqrt{3})
tan
−
1
(
1/
3
)
c.
cot
−
1
(
0
)
\cot^{-1}(0)
cot
−
1
(
0
)
d.
tan
−
1
(
1
)
\tan^{-1}(1)
tan
−
1
(
1
)
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