if a = (2,1,-1) , b= (1,-1,0) , c = (5,-1,1) then unit vector parallel to a + b -c but opposite direction

Options

A. `1/3 (2 hati - hatj + 2hatk)`
B. `1/2(2hati -hatj + 2hatk)`
C. `1/3 (2hati - hatj- 2hatk)`
D. none of these

Answer

A

Explanation

Let a = (2,1,-1) b= (1,-1,0) and c= (5,-1,1)
a +b -c = (2 +1 -5)` hati`
` + (1-1+1) hatj + (-1 + 0 -1) hatk`
` (2hati -hatj + 2hatk)`
Unit vector of
` (a+b-c) = -((2hati - hatj + 2hatk))/3`
Required unit vector of
` (a+b-c) = ((2hati - hatj + 2hatk))/3`