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 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 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 ( vec axx vec b)xx( vec bxx vec c)= vec b ,w h e r e vec a , vec b ,a n d vec c are nonzero vectors, then 1. vec a , vec b ,a n d vec c can be coplanar 2. vec a , vec b ,a n d vec c must be coplanar 3. vec a , vec b ,a n d vec c cannot be coplanar 4.none of these

If ( vec axx vec b)xx( vec cxx vec d) . ( vec axx vec d)=0 , then which of the following may be true? (a) vec a , vec b , vec ca n d vec d are necessarily coplanar (b) vec a lies in the plane of vec ca n d vec d (c) vec b lies in the plane of vec aa n d vec d (d) vec c lies in the plane of vec aa n d vec d

If vec d= vec axx vec b+ vec bxx vec c+ vec cxx vec a is non-zero vector and |( vec d * vec c)( vec axx vec b)+( vec d* vec a)( vec bxx vec c)+( vec d*vec b)( vec cxx vec a)|=0, then a. | vec a|=| vec b|=| vec c| b. | vec a|+| vec b|+| vec c|=|d| c. vec a , vec b ,a n d vec c are coplanar d. none of these

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|

[( vec axx vec b)xx( vec bxx vec c)( vec bxx vec c)xx( vec cxx vec a)( vec cxx vec a)xx( vec axx vec b)] is equal to (where vec a , vec ba n d vec c are nonzero non-coplanar vector) a. [ vec a vec b vec c]^2 b. [ vec a vec b vec c]^3 c. [ vec a vec b vec c]^4 d. [ vec a vec b vec c]

If vec a , vec b , vec c are non-coplanar vector and lambda is a real number, then the vectors vec a+2 vec b+3 vec c ,lambda vec b+mu vec ca n d(2lambda-1) vec c are coplanar when a. mu in R b. lambda=1/2 c. lambda=0 d. no value of lambda

Let vecalpha=a hat i+b hat j+c hat k , vecbeta=b hat i+c hat j+a hat ka n d vecgamma=c hat i+a hat j+b hat k are three coplanar vectors with a!=b ,a n d vec v= hat i+ hat j+ hat kdot Then v is perpendicular to vecalpha b. vecbeta c. vecgamma d. none of these

The pair of lines whose direction cosines are given by the equations 3l+m+5n=0a n d6m n-2n l+5l m=0 are a. parallel b. perpendicular c. inclined at cos^(-1)(1/6) d. none of these