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Question
If `veca = 3hati - 2hatj + hatk` and `vecb = 2hati - 4hatj - 3hatk` then the value of `|veca - 2vecb|` will be ______.
Options
`sqrt(85)`
`sqrt(86)`
`sqrt(87)`
`sqrt(88)`
Solution
If `veca = 3hati - 2hatj + hatk` and `vecb = 2hati - 4hatj - 3hatk` then the value of `|veca - 2vecb|` will be `underlinebb(sqrt(86))`.
Explanation:
Given, `veca = 3hati - 2hatj + hatk`
`vecb = 2hati - 4hatj - 3hatk`
Then, `(veca - 2vecb) = [(3hati - 2hatj + hatk) - 2(2hati - 4hatj - 3hatk)]`
= `[3hati - 2hati + hatk - 4hati + 8hati + 6hati]`
= `(-hati + 6hatj + 7hatk)`
`|veca - 2vecb| = sqrt((-1)^2 + (6)^2 + (7)^2)`
= `sqrt(1 + 36 + 49)`
= `sqrt(86)`
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