[4/2a+b-c=14vec varepsilon,vec a],[2b^(2)c^(2)+2c^(2)a^(2)+2a^(2)b^(2)-a^(4)-b^(4)-c^(4)bar(c)m^(2)+4+vec c],[(a)28]

Prove that 2b^(2)c^(2) +2c^(2)a^(2) +2a^(2)b^(2) -a^(4)-b^(4)-c^(4)= (a+b+c) (b+c-a) (c+a-b) (a+b-c)

Proove that 2b^2c^2+2c^2a^2+2a^2b^2-a^4-b^4-c^4=(a+b+c)(b+a-c)(c+a-b)(a+b-c)

If vec a=mvec b+vec c. The scalar m is (vec c*vec b-vec a*vec c)/(a^(2)) (vec c*vec a-vec b*vec c)/(c^(2)) (vec a*vec b-vec b*vec c)/(b^(2)) (vec a-vec c)/(vec b)

If vec a,vec b and vec c are mutually perpendicular, show that [vec a*(vec b xxvec c)]^(2)=a^(2)b^(2)c^(2)

For any three vectors vec a,vec b,vec c, prove that |vec a+vec b+vec c|^(2)=|vec a|^(2)+|vec b|^(2)+|vec c|^(2)+2(vec adot b+vec bvec c+vec c+vec a)

If vec(a) = 3vec(i) - 2vec(j) + 2vec(i), vec(b) = 6vec(i) + 4vec(j) - 2vec(k), vec(c ) = 3hat(i) - 2hat(j) - 4hat(k) , Then vec(a).(vec(b) xx vec(c )) is

If vec a,vec b and vec c are any three non-coplanar vectors,then prove that points l_(1)vec a+m_(1)vec b+n_(1)vec c,l_(2)vec a+m_(2)vec b+n_(2)vec c,l_(3)vec a+m_(3)vec b+n_(3)vec c,l_(4)vec a+m_(4)vec b+n_(4)vec c are coplanar if [[n_(1),n_(2),n_(3),n_(4)1,1,1,1]]=0