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If the vectors 3 vec p + vec q; 5 vec p ...

If the vectors `3 vec p + vec q`; `5 vec p - 3 vecq` and `2 vec p + vec q`; `4 vec p - 2 vec q` are pairs of mutually perpendicular then sin( `vec p` ^ `vec q)` is :

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We know dot product of two perpendicular vectors is `0`.
`:. (3vecp+vecq).(5vecp-3vecq) = 0`
`=>15|vecp|^2-3|vecq|^2-4vecp*vecq = 0->(1)`
Now, `(2vecp+vecq).(4vecp-2vecq) = 0`
`=>8|vecp|^2-2|vecq|^2 = 0`
`=>|vecq|^2 = 4|vecp|^2`
`=>|vecq| = 2|vecp|`
Putting value of `|vecq|` in (1),
...
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