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Mathematics
Problem
Let
a
=
⟨
a
1
,
a
2
,
a
3
⟩
\mathbf{a}=\langle a_1, a_2, a_3\rangle
a
=
⟨
a
1
,
a
2
,
a
3
⟩
and
b
=
⟨
b
1
,
b
2
,
b
3
⟩
\mathbf{b}=\langle b_1, b_2, b_3\rangle
b
=
⟨
b
1
,
b
2
,
b
3
⟩
. Which of the following equals
a
⋅
b
\mathbf{a}\cdot\mathbf{b}
a
⋅
b
? a)
a
1
2
+
b
1
2
+
a
2
2
+
b
2
2
+
a
3
2
+
b
3
2
a_1^2 + b_1^2 + a_2^2 + b_2^2 + a_3^2 + b_3^2
a
1
2
+
b
1
2
+
a
2
2
+
b
2
2
+
a
3
2
+
b
3
2
b)
a
1
b
2
+
a
2
b
3
+
a
3
b
1
a_1b_2 + a_2b_3 + a_3b_1
a
1
b
2
+
a
2
b
3
+
a
3
b
1
c)
a
1
b
1
+
a
2
b
2
+
a
3
b
3
a_1b_1 + a_2b_2 + a_3b_3
a
1
b
1
+
a
2
b
2
+
a
3
b
3
d)
(
a
1
+
b
1
)
(
a
2
+
b
2
)
(
a
3
+
b
3
)
(a_1 + b_1)(a_2 + b_2)(a_3 + b_3)
(
a
1
+
b
1
)
(
a
2
+
b
2
)
(
a
3
+
b
3
)
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