Let `veca=(1,1,-1), vecb=(5,-3,-3)` and `vecc=(3,-1,2)`. If `vecr` is collinear with `vecc` and has length `(|veca+vecb|)/(2)`, then `vecr` equals

Options

A. `+-3c`
B. `+-(3)/(2)c`
C. `+-c`
D. `+-(2)/(3)c`

Answer

C

Explanation

let `r=lamdac`
Given `|r|=|lamda||c|`
`therefore(|a+c|)/(2)=|lamda||c|`
`therefore|6hati-2hatj-4hatk|=2|lamda|3hati-hatj+2hatk|`
`therefore sqrt(56)=2|lamda|sqrt(14)`
`therefore lamda=+-1`
`therefore r=+-c`.