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  • Show that vector a vector b plus vector b vector a is perpendicular to for any two nonzero vectors .

Q11   Show that   |\vec a | \vec b + |\vec b | \vec a  is perpendicular to   |\vec a | \vec b - |\vec b | \vec a , for any two nonzero vectors  \vec a \: \: \: and \: \: \vec b.

Answers (1)

best_answer

Given in the question that -

 \vec a \: \: \: and \: \: \vec b are two non-zero vectors 

According to the question

\left ( |\vec a | \vec b + |\vec b | \vec a\right )\left (|\vec a | \vec b - |\vec b | \vec a \right )

=|\vec a |^2 |\vec b|^2 - |\vec b |^2 |\vec a|^2+|\vec b||\vec a|\vec a.\vec b-|\vec a||\vec b|\vec b.\vec a=0

Hence |\vec a | \vec b + |\vec b | \vec a  is perpendicular to   |\vec a | \vec b - |\vec b | \vec a.

Posted by

Pankaj Sanodiya

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