Question

If `alpha+beta+gamma =2 and veca=alphahati+betahatj+gammahatk, hatkxx (hatkxxveca)=vec0` then gamma= (A) 1 (B) -1 (C) 2 (D) none of these

Answer 1

Correct Answer - C
Since `(alpha, beta,gamma)` lies on the plane `x+y+z=2`.
`:.alpha+beta+gamma=2`……………i
We have
`hatkxx(hatkxxveca)=vec0`
`implies(hatk.hatk)veca-(hatk.veca)hatk=vec0`
`implies veca-gammahatk=vec0impliesalpha hati+betahatj=vec0impliesalpha=beta=0`
Putting `alpha=beta=0` i (i) we get `gamma=2`.