Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
If
a
×
(
b
×
c
)
\mathbf{a} \times (\mathbf{b} \times \mathbf{c})
a
×
(
b
×
c
)
is perpendicular to
(
a
×
b
)
×
c
(\mathbf{a} \times \mathbf{b}) \times \mathbf{c}
(
a
×
b
)
×
c
, we may have a.
(
a
⋅
c
)
∣
b
∣
2
=
(
a
⋅
b
)
(
b
⋅
c
)
(\mathbf{a} \cdot \mathbf{c})|\mathbf{b}|^2 = (\mathbf{a} \cdot \mathbf{b})(\mathbf{b} \cdot \mathbf{c})
(
a
⋅
c
)
∣
b
∣
2
=
(
a
⋅
b
)
(
b
⋅
c
)
b.
a
⋅
b
=
0
\mathbf{a} \cdot \mathbf{b} = 0
a
⋅
b
=
0
c.
a
⋅
c
=
0
\mathbf{a} \cdot \mathbf{c} = 0
a
⋅
c
=
0
d.
b
⋅
c
=
0
\mathbf{b} \cdot \mathbf{c} = 0
b
⋅
c
=
0
Browse the problem library