If `veca=hati+hatj+2hatkandvecb=2hati+hatj+2hatk`, then find the unit vector in the direction of
(i) `6vecb`
(ii) `2veca-vecb`

Explanation

Here, `veca=hatl+hatj+2hatkandvecb=2hati+hatj-2hatk`
(i) since, `6vecb=12hatl+6hatj-12hatk`
:. Unit vector in the direction of `6vecb=(6vecb)/(|6vecb|)`
`=(12hati+6hatj-12hatk)/(sqrt12^(2)+6^(2)+12^(2))=(6(2hati+hatj-2hatk))/(sqrt324)`
`=(6(2hati+hatj-2hatk))/(18)=(2hatj+hatj-2hatk)/(3)`
(ii) Since, `2veca-vecb=2(hati+hatj+2hatk)-(2hati+hati-2hatk)`
`=2hati+2hatj+4hatk-2hati-hatj+2hatk=hatj+6hatk` :. Unit vector in the direction of `2veca-vecb=(2veca-vecb)/(|2veca-vecb|)=(hatj+6hatk)/(sqrt1+36)=(1)/(sqrt37)(hatj+6hatk)`