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Mathematics
Problem
Prove that for any two vectors
a
,
b
∈
R
3
\mathbf a,\mathbf b\in\mathbb R^{3}
a
,
b
∈
R
3
, the following identity holds:
∣
a
+
b
∣
2
=
∣
a
∣
2
+
∣
b
∣
2
+
2
a
⋅
b
.
|\mathbf a+\mathbf b|^{2}=|\mathbf a|^{2}+|\mathbf b|^{2}+2\,\mathbf a\cdot\mathbf b.
∣
a
+
b
∣
2
=
∣
a
∣
2
+
∣
b
∣
2
+
2
a
⋅
b
.
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