Let `vec a,vec b,vec c` be vectors represented by co-terminous edge of tetrahedron such that `vec a^(^^)vec b=vec b^(^^)vec c=vec c^(^^)vec a=(pi)/(3)` and `|vec a|=sqrt(2);|vec b|=2,|vec c|=3` .The volume of tetrahedron is

Let vec a,vec b,vec c are three vectors along the adjacent edges ofa tetrahedron,if |vec a|=|vec b|=|vec c|=2 and vec a*vec b=vec b*vec c=vec c*vec a=2 then volume of tetrahedron is (A) (1)/(sqrt(2))(B)(2)/(sqrt(3))(C)(sqrt(3))/(2) (D) 2(sqrt(2))/(3)

Let vec a, vec b, vec b, vec b are three vectors such that vec a * vec a = vec b * vec b = vec c * vec c = 3 and | vec a-vec b | ^ (2) + | vec b-vec c | ^ (2) + | vec c-vec a | ^ (2) = 27 then

If vec a,vec b,vec c be three vectors such that |vec a+vec b+vec c|=1,vec c=lambda(vec a xxvec b) and |vec a|=(1)/(sqrt(2)),|vec b|=(1)/(sqrt(3)),|vec c|=(1)/(sqrt(6)), then the angle between vec a and vec b is

If vec a,vec b, and vec c are three vectors such that vec a xxvec b=vec c,vec b xxvec c=vec a,vec c xxvec a=vec b then prove that |vec a|=|vec b|=|vec c|

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

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

If vec a, vec b, vec c are three mutually perpendicular vectors such that | vec a | = | vec b | = | vec c | then (vec a + vec b + vec c) * vec a =

If vec a,vec b and vec c be any three vectors then show that vec a+(vec b+vec c)=(vec a+vec b)+vec c

If vec a, vec b, vec c are three non-coplanar vectors represented by concurrent edges of a parallelopiped of volume 4, (vec a + vec b) + (vec bxx vec c) + (vec b + vec c). ( vec c xx vec a) + (vec c + vec a). (vec axx vec b) is equal to

[vec a + vec b, vec b + vec c, vec c + vec a] = 2 [vec a, vec b, vec c]