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Mathematics
Problem
Identify the correct algebraic formula for the scalar (dot) product of two vectors
a
=
(
a
1
,
a
2
,
a
3
)
\mathbf a=(a_1,a_2,a_3)
a
=
(
a
1
,
a
2
,
a
3
)
and
b
=
(
b
1
,
b
2
,
b
3
)
\mathbf b=(b_1,b_2,b_3)
b
=
(
b
1
,
b
2
,
b
3
)
. a)
a
1
b
2
−
a
2
b
1
a_1 b_2 - a_2 b_1
a
1
b
2
−
a
2
b
1
b)
a
1
2
+
a
2
2
+
a
3
2
b
1
2
+
b
2
2
+
b
3
2
\sqrt{a_1^2+a_2^2+a_3^2}\,\sqrt{b_1^2+b_2^2+b_3^2}
a
1
2
+
a
2
2
+
a
3
2
b
1
2
+
b
2
2
+
b
3
2
c)
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
d)
a
1
2
+
a
2
2
+
a
3
2
a_1^{2}+a_2^{2}+a_3^{2}
a
1
2
+
a
2
2
+
a
3
2
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