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 vecalpha||(vecbxxvecgamma), then (vecalphaxxvecbeta).(vecalphaxxvecgamma)= (A) |vecalpha|^2(vecbeta.vecgamma) (B) |vecbeta|^2(vecgamma.vecalpha) (C) |vecgamma|^2(vecalpha.vecbeta) (D) |vecalpha||vecbeta||vecgamma|

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

Distance of the point P( vec p) from the line vec r= vec a+lambda vec b is a. |( vec a- vec p)+((( vec p- vec a)dot vec b) vec b)/(| vec b|^2)| b. |( vec b- vec p)+((( vec p- vec a)dot vec b) vec b)/(| vec b|^2)| c. |( vec a- vec p)+((( vec p- vec b)dot vec b) vec b)/(| vec b|^2)| d. none of these

vecalpha and vecbeta are two unit vectos and vecr is a vector such that vecr,vecalpha=0 and sqrt(2)(vecrxxvecbeta)=3(vecrxxvecalpha)-vecbeta , then (1)/(|vecr|^(2)) equal

If vec a , vec b , vec c are three given non-coplanar vectors and any arbitrary vector vec r in space, where Delta1=| vec rdot vec a vec bdot vec a vec cdot vec a vec rdot vec b vec bdot vec b vec cdot vec b vec rdot vec c vec bdot vec c vec cdot vec c| , Delta2=| vec adot vec a vec rdot vec a vec cdot vec a vec adot vec b vec rdot vec b vec cdot vec b vec adot vec c vec rdot vec c vec cdot vec c| Delta3=| vec adot vec a vec bdot vec a vec rdot vec a vec adot vec b vec bdot vec b vec rdot vec b vec adot vec c vec bdot vec c vec rdot vec c| , Delta =| vec adot vec a vec bdot vec a vec cdot vec a vec adot vec b vec bdot vec b vec cdot vec b vec adot vec c vec bdot vec c vec cdot vec c| , then prove that vec r=(Delta1)/ Deltavec a+(Delta2)/Delta vec b+(Delta3)/Delta vec c .

If veca=3hati+4hatj+5hatk and vecbeta =2hati+hatj-4hatk , then express vecbeta=vecbeta_1+vecbeta_2 such that vecbeta_1||vecalpha and vecbeta_2botvecalpha .