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Show that | vec a| vec b+| vec b| vec a ...

Show that `| vec a| vec b+| vec b| vec a` is a perpendicular to `| vec a| vec b-| vec b| vec a ,` for any two non-zero vectors ` vec aa n d vec bdot`

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`(|veca|vecb+ |vecb|veca).(|veca|vecb- |vecb|veca)`
=`|veca|^(2)vecb.vecb- |veca||vecb|^(2)vecb.veca`
`+ |vecb||veca|veca.vecb-|veca||vecb|^(2)veca.veca`
`= |veca|^(2)|vecb|^(2)-|vecb|^(2)|veca|^(2)`
=0
Hence, `|veca|vecb + |vecb|veca and |veca|vecb- |vecb|veca` are perpendicular to each other .
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CENGAGE PUBLICATION-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise 2.1
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  6. Let veca , vecb and vecc be pairwise mutually perpendicular vectors, s...

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  9. Let vecu=hati+hatj,vecv=hati-hatj and vecw=hati+2hatj+3hatk. If hatn i...

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  10. A,B,C and d are any four points prove that vec(AB).vec(CD)+vec(BC).vec...

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  11. P(1,0,-1), Q(2,0,-3),R(-1,2,0)a n dS(3,-2,-1), then find the projectio...

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  14. Let vec a , vec ba n d vec c be unit vectors, such that vec a+ vec b...

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