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|`

Answer 1

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.