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