If `vec(a) = 2vec(i) + 3vec(j) + 4vec(k), vec(b)= vec(i) + vec(j)- vec(k), vec(c )= vec(i) - vec(j) + vec(k)` then verify that `vec(a) xx (vec(b) xx vec(c ))` is perpendicular to `vec(a)`

vec(a)= 2vec(i) + vec(j) -vec(k), vec(b)= -vec(i) + 2vec(j)- 4vec(k) and vec(c )= vec(i) + vec(j) + vec(k) , then find (vec(a) xx vec(b)).(vec(b) xx vec(c )) .

If vec(a)= 2vec(i)-vec(j) +vec(k), vec(b)= 3vec(i) + 4vec(j) -vec(k) , then |vec(a) xx vec(b)|=

If 13 vec(a)= 3vec(i) + 4vec(j)+ 12vec(k), 13vec(b)= 4vec(i)-12vec(j) + 3vec(k), 13vec(c )=12vec(i) + 3vec(j)-4vec(k) , then vec(a) xx vec(b) =

If vec(a)= 2vec(i) -vec(j) + 3vec(k), vec(b)= p vec(i) + vec(j) + q vec(k) and vec(b) xx vec(a) = vec(0) , then

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

If vec(a)= 2vec(i) + 3vec(j)- 5vec(k), vec(b)= m vec(i) + n vec(j) + 12 vec(k) and vec(a) xx vec(b) = vec(0) then (m, n)=

(2 vec(i) + 4vec(j) + 2vec(k)) xx (2vec(i) -p vec(j) + 5vec(k))=16 vec(i) -6vec(j) + 2p vec(k) then p=

If vec(a)= 2vec(i)-3 vec(j) + vec(k). vec(b)= vec(i) + 4vec(j)- 2vec(k) , then find (vec(a) + vec(b)) xx (vec(a) - vec(b)) .