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Question
If `hata` is unit vector and `(2vecx - 3hata)*(2vecx + 3hata)` = 91, find the value of `|vecx|`.
Solution
∵ `hata` is a unit vector.
∴ `|hata|` = 1
Given `(2vecx - 3hata)*(2vecx + 3hata)` = 91
`\implies 4vecx*vecx + 6vecx*hata - 6hata*vecx - 9hata*hata` = 91
`\implies 4|vecx|^2 - 9|hata|^2` = 91 ...`[∵ vecx*hata = hata*vecx]`
`\implies 4|vecx|^2 - 9 xx 1` = 91
`4|vecx|^2` = 91 + 9 = 100
`|vecx|^2 = 100/4` = 25
∴ `|vecx| = sqrt(25)` = 5
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