Question

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

Answer 1

We have, `(veca + vecb) xx (veca - vecb) = 8`

⇒ `veca  xx veca - veca xx vecb + vecb xx veca - vecb xx vecb = 8`

but, `veca xx vecb = vecb xx veca`

∴ `veca xx veca - veca xx vecb + veca xx vecb - vecb xx vecb = 8`

= `veca xx veca . vecb xx vecb = 8`

= `64|vecb|^2 - |vecb|^2 = 8`   `[∵ |veca| = 8|vecb|]`

= `63|vecb|^2 = 8`

∴ `|vecb| = sqrt(8/63) = 2/3sqrt(2/7)`

But `|veca| = 8 |vecb|`

⇒ `|veca| = (8sqrt8)/sqrt63`

`= (16sqrt2)/(3sqrt7)`

Hence, `|veca| = (16sqrt2)/(3sqrt7)`

and `|vecb| = (2sqrt2)/(3sqrt7)`