Prove that `(vecbeta-(vecalpha*vecbeta)/(|vecalpha|^2).vecalpha)` is perpendicular to the vector `vec alpha`.

If vec alpha, vec beta, vecgamma be three unit vectors such that |vec alpha+vec beta+vec gamma|=1 and vec alpha is perpendicular to vec beta while vec gamma makes angles theta and phi with vec alpha and vec beta respectively, then the value of cos theta+cos phi is -

If with reference to the right handed system of mutually perpendicular unit vectors hati,hatjandhatk,,vecalpha=3hati-hatj,vecbeta=2hati+hatj-3hatk , then express vecbeta in the form vecbeta=vecbeta_(1)+vecbeta_(2) , where vecbeta_(1) is parallel to vecalphaandvecbeta_(2) is perpendicular to vecalpha .

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+ 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 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|

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

Show that the vector vec(a) is perpendicular to the vector vec(b) - (vec(a).vec(b))/(|vec(a)|^(2))vec(a)

Let vec a , vec b , and vec c are vectors such that | vec a|=3,| vec b|=4 and | vec c|=5, and ( vec a+ vec b) is perpendicular to vec c ,( vec b+ vec c) is perpendicular to vec a and ( vec c+ vec a) is perpendicular to vec bdot Then find the value of | vec a+ vec b+ vec c| .

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