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Mathematics
Mathematics
Problem
For non-zero vectors
a
,
b
,
c
\mathbf{a}, \mathbf{b}, \mathbf{c}
a
,
b
,
c
,
∣
a
×
b
⋅
c
∣
=
∣
a
∣
∣
b
∣
∣
c
∣
|\mathbf{a} \times \mathbf{b} \cdot \mathbf{c}| = |\mathbf{a}||\mathbf{b}||\mathbf{c}|
∣
a
×
b
⋅
c
∣
=
∣
a
∣∣
b
∣∣
c
∣
holds if and only if a.
a
⋅
b
=
0
,
b
⋅
c
=
0
\mathbf{a} \cdot \mathbf{b} = 0, \mathbf{b} \cdot \mathbf{c} = 0
a
⋅
b
=
0
,
b
⋅
c
=
0
b.
b
⋅
c
=
0
,
c
⋅
a
=
0
\mathbf{b} \cdot \mathbf{c} = 0, \mathbf{c} \cdot \mathbf{a} = 0
b
⋅
c
=
0
,
c
⋅
a
=
0
c.
c
⋅
a
=
0
,
a
⋅
b
=
0
\mathbf{c} \cdot \mathbf{a} = 0, \mathbf{a} \cdot \mathbf{b} = 0
c
⋅
a
=
0
,
a
⋅
b
=
0
d.
a
⋅
b
=
b
⋅
c
=
c
⋅
a
=
0
\mathbf{a} \cdot \mathbf{b} = \mathbf{b} \cdot \mathbf{c} = \mathbf{c} \cdot \mathbf{a} = 0
a
⋅
b
=
b
⋅
c
=
c
⋅
a
=
0
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