if ` vecalpha||( vecbetaxx vecgamma)` , then `( vecalphaxxbeta).(vecalphaxx vecgamma)` equals to a.`| vecalpha|^2( vecbeta.vecgamma)` b. `| vecbeta|^2( vecgamma. vecalpha)` c. `| vecgamma|^2( vecalpha. vecbeta)` d. `| vecalpha|| vecbeta|| vecgamma|`

Prove that vec R+([ vec Rdot( vecbetaxx( vecbetaxx vecalpha))] vecalpha)/(| vecalphaxx vecbeta|^2) +([ vec Rdot( vecalphaxx( vecalphaxx vecbeta))] vecbeta)/(| vecalphaxx vecbeta|^2) =([ vec R vecalpha vecbeta]( vecalphaxx vecbeta))/(| vecalphaxx vecbeta|^2)

If vec a is parallel to vec bxx vec c , then ( vec axx vec b) . ( vec axx vec c) is equal to a. | vec a|^2( vec b . vec c) b. | vec b|^2( vec a . vec c) c. | vec c|^2( vec a . vec b) d. none of these

If vecalpha+ vecbeta+ vecgamma=a vecdeltaa n d vecbeta+ vecgamma+ vecdelta=b vecalpha, vecalphaa n d vecdelta are non-colliner, then vecalpha+ vecbeta+ vecgamma+ vecdelta equals a. a vecalpha b. b vecdelta c. 0 d. (a+b) vecgamma

If vectors vecalpha,vecbeta, vecgamma are such that vecalpha+vecbeta+vec gamma=vec0 and |veca|=2, |vecbeta|=3 and |vecgamma|=4 , then the value of 2(vecalpha*vecbeta+vecbeta*vecgamma+vecgamma*vecalpha) is -

If a(vecalpha xx vecbeta) + b(vecbeta xx vecgamma) +c(vecgamma xx vecalpha)=veco , where a, b, c are non-zero scalars, then the vectors vecalpha, vecbeta, vecgamma are

Let vecalpha, vecbeta, vecgamma be three non-zero vectors which are pairwise non-collinear. If vecalpha+3vecbeta is collinear with vecgamma and vecbeta +2vecgamma is collinear with vecalpha , then vecalpha+3vecbeta +6vecgamma is

If a( vecalphaxx vecbeta)+b( vecbetaxx vecgamma)+c( vecgammaxx vecalpha)=0 and at least one of a ,ba n dc is nonzero, then vectors vecalpha, vecbetaa n d vecgamma are a. parallel b. coplanar c. mutually perpendicular d. none of these

If vec alpha = lambda hat i+hatj+3 hatk,vec beta= -hati+2hatj+hatk,vecgamma=3hati+hatj+2hatk and [vecalpha vecbeta vecgamma]=-10 find the value of lambda .

A parallelogram is constructed on the vectors veca=3vecalpha-vecbeta, vecb=vecalpha+3vecbeta. If |vecalpha|=|vecbeta|=2 and angle between vecalpha and vecbeta is pi/3 then the length of a diagonal of the parallelogram is