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Mathematics
Mathematics
Problem
Show that for any two vectors
a
,
b
∈
R
3
\mathbf{a},\mathbf{b}\in\mathbb{R}^3
a
,
b
∈
R
3
, the identity
∣
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
holds.
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