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Mathematics
Mathematics
Problem
The edges of a parallelepiped are of unit length and are parallel to non-coplanar unit vectors
a
^
,
b
^
,
c
^
\hat{a}, \hat{b}, \hat{c}
a
^
,
b
^
,
c
^
such that
a
^
⋅
b
^
=
b
^
⋅
c
^
=
c
^
⋅
a
^
=
1
2
\hat{a} \cdot \hat{b} = \hat{b} \cdot \hat{c} = \hat{c} \cdot \hat{a} = \frac{1}{2}
a
^
⋅
b
^
=
b
^
⋅
c
^
=
c
^
⋅
a
^
=
2
1
. Find the volume of the parallelepiped. a.
1
2
\frac{1}{\sqrt{2}}
2
1
cu unit b.
1
2
2
\frac{1}{2\sqrt{2}}
2
2
1
cu unit c.
3
2
\frac{\sqrt{3}}{2}
2
3
cu unit d.
1
3
\frac{1}{\sqrt{3}}
3
1
cu unit
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