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 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

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 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|

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

Statement 1: vec a , vec b ,a n d vec c are three mutually perpendicular unit vectors and vec d is a vector such that vec a , vec b , vec ca n d vec d are non-coplanar. If [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a]=1,t h e n vec d= vec a+ vec b+ vec c . Statement 2: [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a] ; then vec d equally inclined to vec a , vec b and vec c . (a) statement 1 is true but statement 2 is false. (b) statement 2 is true but statement 1 is false. (c)both the statements are true. (d) both the statements are false.

Let vec a , vec b ,a n d vec c be non-zero vectors and vec V_1= vec axx( vec bxx vec c)a n d vec V_2=( vec axx vec b)xx vec c. Vectors vec V_1a n d vec V_2 are equal. Then (a). vec aa n vec b are orthogonal (b). vec aa n d vec c are collinear (c). vec ba n d vec c are orthogonal (d). vec b=lambda( vec axx vec c)w h e nlambda is a scalar

If vec a\ a n d\ vec b are two vectors such that | vec axx vec b|=sqrt3\ a n d\ vec adot vec b=1, find the angle between vec a\ a n d\ vec b .

If vec a , vec b , vec ca n d vec d are distinct vectors such that vec axx vec c= vec bxx vec da n d vec axx vec b= vec cxx vec d , prove that ( vec a- vec d). (vec b- vec c)!=0,