Question

If `veca = hati  +hatj + hatk, vecb = 2hati - hatj +  3hatk and vecc = hati - 2hatj + hatk` find a unit vector parallel to the vector `2veca - vecb + 3vecc`.

Answer 1

We have,

`veca = hati + hatj + hatk, `

`vecb = 2hati - hatj + 3hatk, `

`vecc = hati - 2hatj + 3hatk`

`= 2veca - vecb + 3vecc = 2(hati + hatj + hatk) - (2hati - hatj + 3hatk) + 3(hati - 2hatj + hatk)`

= `3hati - 3hatj + 2hatk`

= `|2veca - vecb + 3vecc|`

`= sqrt(3^2 + (-3)^2 + 2^2)`

`= sqrt(9 + 9 + 4)`

`= sqrt22`

Hence with the unit vector `2veca - vecb + 3vecc`

`(2veca - vecb + 3vecc)/|2veca - vecb + 3vecc| = ((3hati - 3hatj + 2hatk))/sqrt22`

`= 3/sqrt22hati - 3/sqrt22hatj + 2/sqrt22hatk`