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 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 (a) vec a , vec b ,a n d vec c can be coplanar (b) vec a , vec b ,a n d vec c must be coplanar (c) vec a , vec b ,a n d vec c cannot be coplanar (d)none of these

If ( vec axx vec b)xx( vec cxx vec d)dot( 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

[( 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) [ 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 O+ vec O B= vec B O+ vec O C , then A ,Bn a dC are (where O is the origin) a. coplanar b. collinear c. non-collinear d. none of these

if vecalpha||( vecbetaxx vecgamma) , then ( vecalphaxxbeta)dot( vecalphaxx vecgamma) equals to | vecalpha|^2( vecbetadot vecgamma) b. | vecbeta|^2( vecgammadot vecalpha) c. | vecgamma|^2( vecalphadot vecbeta) d. | vecalpha|| vecbeta|| vecgamma|

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

If three unit vectors vec a , vec b ,a n d vec c satisfy vec a+ vec b+ vec c=0, then find the angle between vec aa n d vec bdot