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Mathematics
Mathematics
Problem
For any three vectors
a
⃗
\vec{a}
a
,
b
⃗
\vec{b}
b
,
c
⃗
\vec{c}
c
, prove that
∣
a
⃗
+
b
⃗
+
c
⃗
∣
2
=
∣
a
⃗
∣
2
+
∣
b
⃗
∣
2
+
∣
c
⃗
∣
2
+
2
(
a
⃗
⋅
b
⃗
+
b
⃗
⋅
c
⃗
+
c
⃗
⋅
a
⃗
)
|\vec{a} + \vec{b} + \vec{c}|^2 = |\vec{a}|^2 + |\vec{b}|^2 + |\vec{c}|^2 + 2(\vec{a} \cdot \vec{b} + \vec{b} \cdot \vec{c} + \vec{c} \cdot \vec{a})
∣
a
+
b
+
c
∣
2
=
∣
a
∣
2
+
∣
b
∣
2
+
∣
c
∣
2
+
2
(
a
⋅
b
+
b
⋅
c
+
c
⋅
a
)
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