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Find |veca|and|vecb|, if (veca+vecb)*(ve...

Find `|veca|and|vecb|`, if `(veca+vecb)*(veca-vecb)=8and|veca|=8|vecb|`.

Text Solution

Verified by Experts

`(veca+vecb) .(veca-vecb) =8`
`or veca.veca-veca.vecb+vecb.veca-vecb.vecb=8`
`or |veca|^(2) -|vecb|^(2)=8`
`or (8|vecb|)^(2)-|vecb|^(2)=8 " " [|veca|=8|vecb|]`
`or |vecb|=sqrt(8/63)`
`or |veca|=8|vecb|=(8xx2sqrt2)/(3sqrt7)= (16sqrt2)/(3sqrt7)`
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Knowledge Check

  • If |veca|=5|vecb|=4 and |veca+vecb|=1 then |veca-vecb|= ?

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    B
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