Find the angle between the following vectors: `(i) vec(a)=vec(i)+2vec(j)+2vec(k)`, `vec(b)=vec(i)-2vec(j)+2vec(k)`

Find the angle between the vectors : vec(a)=3vec(i)-2vec(j)+vec(k) and vec(b)=vec(i)-2vec(j)-3vec(k)

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

Find the angle between the planes vec(r).(2vec(i)-vec(j)+2vec(k))=3 an vec(r).(3vec(i)+6vec(j)+vec(k))=4 .

Find a vector of magnitude and perpendicular to both the vectors vec(a)= 2vec(i)- 2vec(j) + vec(k) and vec(b)= 2vec(i) + 2vec(j) + 3vec(k)

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

Equation of the plane containing the lines vec(r )= vec(i) + 2vec(j) -vec(k) + lamda (vec(i) + 2vec(j)-vec(k)), vec(r )=vec(i) + 2vec(j) -vec(k)+ mu (vec(i) + vec(j) + 3vec(k)) is

The value of lambda for two perpendicular vectors vec(A)=2vec(i)+lambdavec(j)+vec(k) and vec(B)=4vec(i)-2vec(j)-2vec(k) is :-

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

If vec(c ) is a unit vector perpendicular to both vec(a) = vec(i) + 5vec(j) + vec(k) and vec(b)= 2vec(i) - vec(j) + vec(k) such that vec(a), vec(b), vec(c ) form right handed system then find vec(c ) .