Question

Plz solve this fast
I will mark them as brainlest

Answer 1

$\pink{\ \boxed{\boxed{\begin{array}{cc} \bf \:L.H.S = ( \vec{A} - \vec{B}) \times ( \vec{A} + \vec{B}) \\ \\ \bf \: = \vec{A} \times ( \vec{A} + \vec{B}) - \vec{B} \times ( \vec{A} + \vec{B}) \\ \\ \bf \: = \vec{A} \times \vec{A} + \vec{A}\times \vec{B} - \vec{B} \times \vec{A} - \vec{B} \times \vec{B} \\ \\ \bf = \vec{0} +\vec{A}\times \vec{B} - \{ - (\vec{A}\times \vec{B}) \} - \vec{0} \\ \\ \orange{{\boxed{\begin{array}{cc} \maltese \bf \: \: \because\: \: \vec{A}\times \vec{B} = - (\vec{B }\times \vec{A}) \\\vec{A}\times \vec{A} = \vec{0} \\\vec{B}\times \vec{B} = \vec{0}\end{array}}}} \\ \\ \bf =\vec{A}\times \vec{B} + \vec{A}\times \vec{B} \\ \\ \bf= 2(\vec{A}\times \vec{B}) \\ \\ = \bf \: R.H.S \end{array}}}}$