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Question
Evaluate the product `(3veca - 5vecb).(2veca + 7vecb)`.
Solution
We have, `(3veca - 5vecb) . (2veca + 7vecb)`
`= (3veca) xx (2veca) + (3veca) xx (7vecb) + (-5vecb) xx (2veca) + (-5vecb) xx (7vecb)`
= `6|veca|^2 + 21(veca xx vecb) - 10(vecb xx veca) - 35|vecb|^2` `[∵ veca xx vecb = vecb xx veca]`
= `6|veca|^2 + 21(veca xx vecb) - 10(veca xx vecb) - 35|vecb|^2`
= `6|veca|^2 + 11(veca xx vecb) - 35|vecb|^2`
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