It is presumed that you are familiar with vector multiplication.

Here are some questions to ask yourself as a refresher:

A
⃗
⋅
B
⃗
A
⃗
⋅
B
⃗
.
Is it a vector or a scalar?

Answer: scalar
A
⃗
⋅
B
⃗
=
A
x
B
x
+
A
y
B
y
+
A
z
B
z
A
⃗
⋅
B
⃗
=
A
x
B
x
+
A
y
B
y
+
A
z
B
z

A
⃗
×
B
⃗
A
⃗
×
B
⃗
.
Is it a vector or a scalar?

Answer: Vector
(
A
⃗
×
B
⃗
)
x
=
A
y
B
z
−
A
z
B
y
(
A
⃗
×
B
⃗
)
y
=
A
z
B
x
−
A
x
B
z
(
A
⃗
×
B
⃗
)
z
=
A
x
B
y
−
A
y
B
x
(
A
⃗
×
B
⃗
)
x
=
A
y
B
z
−
A
z
B
y
(
A
⃗
×
B
⃗
)
y
=
A
z
B
x
−
A
x
B
z
(
A
⃗
×
B
⃗
)
z
=
A
x
B
y
−
A
y
B
x

What is
A
⃗
×
A
⃗
A
⃗
×
A
⃗

Answer: 0

What is
A
⃗
⋅
(
A
⃗
×
B
⃗
)
A
⃗
⋅
(
A
⃗
×
B
⃗
)

Answer: 0

Another useful thing to
remember
A
⃗
⋅
(
B
⃗
×
C
⃗
)
=
(
A
⃗
×
B
⃗
)
⋅
C
⃗
A
⃗
⋅
(
B
⃗
×
C
⃗
)
=
(
A
⃗
×
B
⃗
)
⋅
C
⃗
=
(
C
⃗
×
A
⃗
)
⋅
B
⃗
=
(
C
⃗
×
A
⃗
)
⋅
B
⃗
This
is the scalar triple product which is the volume of a parallelopiped whose
edges are given by
A
⃗
,
B
⃗
,
C
⃗
A
⃗
,
B
⃗
,
C
⃗
.

Comments:"This book covers second year Physics at Rice University."