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Find |veca| and |vecb| if (veca+vecb).(v...

Find `|veca| and |vecb| if (veca+vecb).(veca-vecb)=8 and |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|=|vecb| , then (veca+vecb).(veca-vecb) is equal to

    A
    Positive
    B
    Negative
    C
    Zero
    D
    None of these

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    A
    `vec|b|=46`
    B
    `vec|b|=48`
    C
    `vec|b|=44`
    D
    `vec|b|=50`

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