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Question
Find `|vecx|` if `(vecx - veca).(vecx + veca)` = 12, where `veca` is a unit vector.
Solution
Since `veca` is a unit vector
∴ `|veca|` = 1
`(vecx - veca).(vecx + veca)` = 12
⇒ `vecx.vecx + vecx.veca - veca.vecx - veca.veca` = 12
⇒ `|vecx|^2 - |veca|^2` = 12
⇒ `|vecx|^2 - 1` = 12
⇒ `|vecx|^2` = 13
⇒ `|vecx| = sqrt(13)`
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