1.

For any three vectors `veca, vecb, vecc` the value of `[(veca-vecb, vecb-vecc, vecc-veca)]`, isA. `0`B. `[(veca, vecb, vecc)]`C. `-[(veca, vecb, vecc)]`D. `-2[(veca, vecb, vecc)]`

Answer» Correct Answer - A
Let `vec(alpha)=veca-vecb, vec(beta)=vecb-vecc` and `vec(gamma)=vecc-veca`
or `vec(alpha)=veca-vecb+0vecc, vec(beta)=0veca+vecb-vecc` and `vec(gamma)=-veca+0vecb+vecc`
Then
`[(vec(alpha), vec(beta), vec(gamma))]=|(1,-1,0),(0,1,-1),(-1,0,1)|[(veca, vecb, vecc)]`
`implies[(vec(alpha),vec(beta),vec(gamma))]=0[(veca, vecb, vecc)]=0`
Alter 1 We have
`vec(alpha)+vec(beta)+vec(gamma)=veca-vecb+vecb-vecc+vecc-veca=vec0`
`impliesvec(alpha),vec(beta),vec(gamma)` are coplanar.
`implies[(vec(alpha), vec(beta), vec(gamma))=0` or `[(veca-vecb,vecb-vecc, vecc-veca)]=0`


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