If vectors ` vec a , vec b ,a n d vec c` are coplanar, show that `| vec a vec b vec c vec adot vec a vec adot vec b vec adot vec c vec bdot vec a vec bdot vec b vec bdot vec c|=odot`

If the vectors vec a, vec b, vec c are coplanar, then the value of | (vec a, vec b, vec c), (vec a * vec a, vec a * vec b, vec a * vec c), (vec b * vec a, vec b * vec b, vecb * vec c) | =

If vec a, vec b, vec c are coplanar vectors, then | vec a, vec b, vec cvec b, vec c, vec avec b, vec a, vec b] | = vec a

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 .

The vectors vec a,vec b,vec c,vec d are coplanar then

vec a, vec b ,, vec c are coplanar vectors, prove that vec a, vec b, vec cvec with a, vec with b, vec a, vec with bvec a, vec bvec b, vec b, vec a] | = 0

The condition for equations vec rxx vec a= vec ba n d vec rxx vec c= vec d to be consistent is vec bdot vec c= vec adot vec d b. vec adot vec b= vec cdot vec d c. vec bdot vec c+ vec adot vec d=0 d. vec adot vec b+ vec cdot vec d=0

If vec a, vec b and vec c are non coplaner vectors such that vec b xxvec c = vec a, vec c xxvec a = vec b and vec a xxvec b = vec c then | vec a + vec b + vec c | =

If vec a= hat i+ hat j+ hat k , vec b= hat i- hat j+ hat k , vec c= hat i+2 hat j- hat k , then find the vaue of | vec adot vec a vec adot vec b vec adot vec c vec bdot vec a vec bdot vec a vec bdot vec a vec cdot vec a vec cdot vec a vec cdot vec a| .

If vec a,vec b,vec c are unit vectors such that vec a+vec b+vec c=vec 0 find the value of vec a+vec b+vec bdot c+vec *vec a

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] =>vec d is equally inclined to veca,vecb,vecc.