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Prove that \[(\overrightarrow{a}+\overrightarrow{b}).(\overrightarrow{a}-\overrightarrow{b})={{\left| \overrightarrow{a} \right|}^{2}}+{{\left| \overrightarrow{b} \right|}^{2}}\], if and only if \[\overrightarrow{a}\] , \[\overrightarrow{b}\] are perpendicular, given\[\overrightarrow{a}\ne 0,\overrightarrow{b}\ne 0\].
Prove that \[(\overrightarrow{a}+\overrightarrow{b}).(\overrightarrow{a}-\overrightarrow{b})={{\left| \overrightarrow{a} \right|}^{2}}+{{\left| \overrightarrow{b} \right|}^{2}}\], if and only if \[\overrightarrow{a}\] , \[\overrightarrow{b}\] are perpendicular, given\[\overrightarrow{a}\ne 0,\overrightarrow{b}\ne 0\].
CBSE | Class 12 | Maths | Miscellaneous | NCERT | Vector Algebra
Prove that \[(\overrightarrow{a}+\overrightarrow{b}).(\overrightarrow{a}-\overrightarrow{b})={{\left| \overrightarrow{a} \right|}^{2}}+{{\left| \overrightarrow{b} \right|}^{2}}\], if and only if \[\overrightarrow{a}\] , \[\overrightarrow{b}\] are perpendicular, given\[\overrightarrow{a}\ne 0,\overrightarrow{b}\ne 0\].

It is given that

Hence proved.

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