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Question
If `veca` is a nonzero vector of magnitude 'a' and λ a nonzero scalar, then λ`veca` is unit vector if ______.
Options
λ = 1
λ = -1
a = |λ|
`a = 1/|λ|`
Solution
If `veca` is a nonzero vector of magnitude ‘a’ and λ a nonzero scalar, then λ`veca` is unit vector if `underline(a = 1/|λ|)`
Explanation:
Given : Resultant of `veca` = a
That is, `|veca| = a`
`λveca` is a unit vector
`|lambdaveca| = 1`
`|lambda||veca| = 1`
`|lambda|a = 1``
`a = 1/|lambda|`
Hence, option `a = 1/|lambda|` is correct.
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