If `vec A xx vec B= vec C xx vec B`, show that `vec C` need not be equal to vec A`.

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

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

If vec A xx vec B=vec A xx vec C , is it correct to conclude that vec B =vec C ?

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

If vec A, vec B and vec C are vectors such that |vec B|-|vec C| . Prove that [(vec A+ vec B)xx (vec A + vec C)]xx (vec B+vec C).(vec B+ vec C)=0

If vec A, vec B and vec C are vectors such that |vec B|=|vec C| . Prove that [(vec A+ vec B)xx (vec A + vec C)]xx (vec B+vec C).(vec B+ vec C)=0

If vec A, vec B and vec C are vectors such that |vec B|=|vec C| . Prove that [(vec A+ vec B)xx (vec A + vec C)]xx (vec B+vec C).(vec B+ vec C)=0

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 .

If vec(a) xx vec(b) = vec(c ) xx vec(d) and vec(a) xx vec(c )= vec(b) xx vec(d) then show that vec(a)- vec(d) and vec(b) -vec(c ) are parallel vectors.

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 vec(b) - vec (c) , where to vec (a) != vec (d) and vec ( b) != vec (c )