सिद्ध करें कि (a - b) x (a + b) = 2(a x b)

Question

सिद्ध करें कि \((\vec a - \vec b) \times (\vec a + \vec b) = 2(\vec a \times \vec b)\)

Answer 1

\((\vec{a}-\vec{b}) \times(\vec{a}+\vec{b})=2(\vec{a} \times \vec{b})\)

बायाँ पक्ष \(=(\vec{a}-\vec{b}) \times(\vec{a}+\vec{b})\)

\(=(\vec{a} \times \vec{a})+(\vec{a} \times \vec{b})-(\vec{b} \times \vec{a})-(\vec{b} \times \vec{b})\)

\(=0+\vec{a} \times \vec{b}-\vec{b} \times \vec{a}-0\)

\(=0+\vec{a} \times \vec{b}+\vec{a} \times \vec{b}\)

\(=2(\vec{a} \times \vec{b})\)

= दायाँ पक्ष सिद्ध हुआ।