If `[vecb" "vec(c)" "vecd]+[vec(c)" "vec(a)" "vecd]+[vec(a)" "vecb" "vecd]=[a" "b" "c]` then show that the points with position vectors a,b,c and `vecd` are coplanar.

If vec(a) xx vec(b)= vec(c ) xx vec(d), vec(a) xx vec(c )= vec(b) xx vec(d) , then

Let vec(C ) = vec(A) + vec(B) ,

If vec(a).vec(b) = vec(a).vec(c ) and vec(a) xx vec(b)= vec(a) xx vec(c ) and vec(a) ne vec(0) then show that vec(b)= vec(c )

If vec(C) = vec(A) + vec(B) then

If veca,vecb,vec(c) are non-coplanar, then show that the vectors veca-vecb,vecb+vec(c),vec(c)+vec(a) are planar.

Let vec(a), vec(b), vec(c ) be such that vec(c ) ne vec(0), vec(a) xx vec(b)= vec(c ) and vec(b) xx vec(c )= vec(a) then show that vec(a), vec(b) and vec(c ) are pairwise perpendicular, |vec(b)|=1 and |vec(c )|= |vec(a)| .

If vec(a) xx vec(b) = vec(b) xx vec(c )= vec(c )xx vec(a) , where vec(a), vec(b), vec(c ) are non zero vectors, then