`vec a xx vec b=vec a xx vec c` where `(a != 0)` implies that `b=c`

If vec a ,\ vec b ,\ vec c are three vectors such that vec a. vec b= vec a.\ vec c and vec a\ xx\ vec b= vec a\ xx\ vec c ,\ vec a\ !=0 , then show that vec b= vec c .

(vec b xx vec c) xx (vec c xx vec a ) =

If vec a xx vec b = vec c and vec b xx vec c = vec a then

For vectors vec(a),vec(b) and vec( c ),vec(a).vec(b)=vec(a).vec( c ) and vec(a)xx vec(b)=vec(a)xx vec( c ),vec(a) ne vec(0) then show that vec(b)=vec( c ) .

If three vectors vec A, vec B and vec C are such that vec A .vec B =vec A .vec C , vec A xx vec B = vec A xx vec C , vec A!= vec 0 then prove that vec B =vec C .

(vec a-vec b)*{(vec b-vec c)xx(vec c-vec a)}=0

If (vec a xx vec b) xx vec c = vec a xx (vec b xx vec c) , where vec a, vec b and vec c are any three vectors such that vec a. vec b ne 0, vec b . vec c ne 0 , then vec a and vec c are

If vec a\ xx\ vec b=\ vec c\ xx\ vec d\ and vec a\ xx\ vec c=\ vec b\ xx vec d show that vec a- vec d is parallel to vec b- vec c , where vec a!= vec d and vec b!= vec c

Solve the following equation for the vector vec p; vec p xx vec a+(vec p. vec b)vec c=vec b xx vec c where vec a ,vec b,vec c are non zero non coplanar vectors and vec a is neither perpendicular to vec b non to vec c hence show that (vec p xx vec a+([vec a vec b vec c])/(vec a*vec c) vec c) is perpendicular vec b-vec c.

(vec a xxvec b)xxvec c=vec a xx(vec b xxvec c), Where vec a,vec b and vec c and any three vectors such that vec a*vec b=0,vec b*vec c=0 then vec a and vec c are