If a + b + c = 0, then prove that a . b = b . c = c . a

Question

If \(\vec{a}+\vec{b}+\vec{c}=0,\) then prove that \(\vec{a}\times \vec{b}=\vec{b}\times \vec{c}=\vec{c}\times \vec{a}\)

Answer 1

[By the distributive law]

[By the distributive law]

From (i) and (ii), we get \((\vec{a}\times \vec{b})=(\vec{b}\times \vec{c})=(\vec{c}\times \vec{a}).\)