If `vec(a) + 2vec(b) + 4vec(c ) = vec(0)` then show that `vec(a) xx vec(b) =4 (vec(b) xx vec(c ))= 2(vec(c ) xx vec(a))`

(vec(a) xx vec(b), vec(b) xx vec(a)) =

If vec(a) + 2vec(b) + 4 vec(c )= vec(0) , then vec(a) xx vec(b) + vec(b) xx vec(c )+ vec(c )xx vec(a)=

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

Let vec(a) + m vec(b) + n vec(c )= vec(0).vec(a) xx vec(b) + vec(b) xx vec(c ) + vec(c ) xx vec(a)= vec(0) for

If vec(a) + vec(b) + vec(c )= vec(0) and |vec(a) xx vec(b)|=3 , then |vec(b) xx vec(c )| =

If vec(a)= -vec(i) + vec(j) + vec(k), vec(b)= vec(i)-vec(j) + vec(k), vec(c )= vec(i) + vec(j)-vec(k) , then the vectors vec(a) xx vec(b), vec(b) xx vec(c ), vec(c ) xx vec(a) are

If the vectors vec(a), vec(b), vec(c ) form the sides vec(BC), vec(CA), vec(AB) respectively of triangle ABC then show that vec(a) xx vec(b) = vec(b)xx vec(c ) = vec(c ) xx vec(a) .

If vec(a) = 7vec(i) -2vec(j) + 3vec(k), vec(b)= 2vec(i) + 8vec(k), vec(c ) =vec(i) + vec(j) + vec(k) , then verify that vec(a) xx (vec(b) + vec(c ))= (vec(a) xx vec(b)) + (vec(a) xx vec(c )) (or) prove that cross product is distributive over addition

If vec(a)= vec(i) + vec(j) + vec(k), vec(b)= 2vec(i)-3vec(j) + vec(k) , then (vec(a) xx vec(b))/(|vec(a) xx vec(b)|) + (vec(b) xx vec(a))/(|vec(b) xx vec(a)|) =

If three vectors vec(a), vec(b), vec(c ) are such that vec(a) ne vec(0) and vec(a) xx vec(b)=2 (vec(a) xx vec(c )), |vec(a)| = |vec(c )| =1, |vec(b)|=4 and the angle between vec(b) and vec(c ) is cos^(-1) ((1)/(4)) , then vec(b)-2vec(c )= lamda vec(a) where lamda =