A non-zero vector ` vec a` is such that its projections along vectors `( hat i+ hat j)/(sqrt(2)),(- hat i+ hat j)/(sqrt(2))` and ` hat k` are equal, then unit vector along ` vec a` is a.`(sqrt(2) hat j- hat k)/(sqrt(3))` b. `( hat j-sqrt(2) hat k)/(sqrt(3))` c. `(sqrt(2))/(sqrt(3)) hat j+( hat k)/(sqrt(3))` d. `( hat j- hat k)/(sqrt(2))`

Options

A. `(sqrt2hatj-hatk)/sqrt3`
B. `(hatj-sqrt2hatk)/sqrt3`
C. `sqrt2/sqrt3hatj+hatk/sqrt3`
D. `(hatj - hatk)/(sqrt2)`

Answer

a

Explanation

Let the projection be x then ,
`veca= (x(hati +hatj))/sqrt2+(x(-hati+hatj))/sqrt2+xhatk`
`veca= (2xhatj)/sqrt2+ xhatk or hata= sqrt2/sqrt3hatj + hatk/sqrt3`