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Question
If two vectors `veca` and `vecb` are such that `|veca|` = 2, `|vecb|` = 3 and `veca.vecb` = 4, then `|veca - 2vecb|` is equal to ______.
Options
`sqrt(2)`
`2sqrt(6)`
24
`2sqrt(2)`
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Solution
If two vectors `veca` and `vecb` are such that `|veca|` = 2, `|vecb|` = 3 and `veca.vecb` = 4, then `|veca - 2vecb|` is equal to `underline(bb(2sqrt(6))`.
Explanation:
`|veca - 2vecb|^2 = (veca - 2vecb).(veca - 2vecb)`
`|veca - 2vecb|^2 = veca.veca - 4veca.vecb + 4vecb.vecb`
= `|veca|^2 - 4veca.vecb + 4|vecb|^2`
= 4 – 16 + 36 = 24
`|veca - 2vecb|^2` = 24
⇒ `|veca - 2vecb| = 2sqrt(6)`
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