The vector in the direction of the vector `hati-2hatj+2hatk` that has magnitude 9 is

Options

A. `hati-2hatj+2hatk`
B. `(hati-2hatj+2hatk)/(3)`
C. `3(hati-2hatj+2hatk)`
D. `9(hati-2hatj+2hatk)`

Answer

C

Explanation

Let `veca=hati-2hatj+2hatk`
Any vector in the dirction of a vector `veca` is given by `veca/(|veca|)`,
`(hati-2hatj+2hatk)/(sqrt(1^(2)+2^(2)+2^(2)))=(hati-2hatj+2hatk)/(3)`
:. Vector in the direction of `veca` with magnitude `9=9.(hati-2hatj+2hatk)/(3)`
`=3(hati-2hatj+2hatk)`