The vector area of the triangle formed by the points `vec(i) -vec(j) + vec(k), 2vec(i) + vec(j) -2vec(k) and 3vec(i) + vec(j) + 2vec(k)` is

The area of the triangle formed by thepoints whose position vectors are 3vec(i) + vec(j), 5vec(i) + 2vec(j) + vec(k) and vec(i) -2vec(j) + 3vec(k) is (in sq.u)

The vector area of the parallelogram whose diagonals are vec(i) + 2vec(j) + 3vec(k), -vec(i) - 2vec(j) + vec(k) is

The vector area of the parallelogram whose adjacent sides vec(i) + vec(j) + vec(k) and 2vec(i)-vec(j) + 2vec(k) is

Find the vector equation of the plane passing through the points. vec(i)-2vec(j)+5vec(k), -5vec(j)-vec(k) and -3vec(j)+5 vec(j) .

(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=

Find the angle between the vectors vec(i) + 2vec(j) + 3vec(k) and 3vec(i) - vec(j) + 2vec(k) .

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

A unit vector normal to the plane through the points vec(i), 2vec(j) and 3vec(k) is

A unit vector perpendicular to 2vec(i) + 3vec(j) + 4vec(k) and 3vec(j) + 2vec(k) is

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