A non-zero vecto veca is such tha its pr...

A non-zero vecto `veca` is such tha its projections along vectors `(hati + hatj)/sqrt2, (-hati + hatj)/sqrt2 and hatk` are equal , then unit vector along `veca` us

A

`(sqrt2hatj-hatk)/sqrt3`

B

`(hatj-sqrt2hatk)/sqrt3`

C

`sqrt2/sqrt3hatj+hatk/sqrt3`

D

`(hatj - hatk)/(sqrt2)`

Text Solution

Verified by Experts

The correct Answer is:

a

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`

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