Find the unit vector in the direction of the vector `vec a + vec b if vec a =vec i +2 vec j + 3 vec k and vec b = 2 vec i + 3 vec j + 5 vec k`.

Find the unit vector in the direction of vec a+vec b,quad if quad vec a=2hat i-hat j+2hat k and vec b=-hat i+hat j-hat k

Let vec a = hat i + hat j + hat k, vec b = hat i + 4 hat j - hat k, vec c = hat i + hat j + 2 hat k and hat s be a the unit vector the magnitude of the vector (vec a .vec s)(vec b xx vec c) + (vec b. vec s)(vec c xx vec a) + ( vec c.vec s)(vec a xx vec b) is equal to (A) 1 (B) 2 (C) 3 (D) 4

Find a unit vector which is perpendicular to each of the vectors 3vec i+2vec j-vec k and 12vec i+5vec j-5vec k

What is the unit vector hat a parallel to the vector vec a= 3 vec I + 4 vec j - 2 vec k ? Find the vector vec b such that hat a + vec b becomes the unit vector vec i ?

Find lambda such that the scalar product of the vector vec i + vec j + vec k with the unit vector parallel to the sum of the vectors 2 vec i + 4 vec j - 5 vec k and lambda vec i + 2 vec j + 3 vec k is equal to 1.

The position vectors of the points A,B,C , D are respectively 2 vec i + vec j - vec k, vec i + vec j + vec k, vec i- 2 vec j+ 3 vec k and 3 vec i- vec j + 2 vec k . Evaluate [vec (AB), vec (AC), vec (AD)] .

If | vec a | = 2, | vec b | = 7 and vec a xxvec b = 3vec i + 2vec j + 6vec k then vec a * vec b =

If vec r = 3vec i + 2vec j-5vec kvec a = 2vec i-vec j + vec k, vec b = vec i + 3vec j-2vec k and vec c = -2vec i + vec j-3vec k such that vec r = lambdavec a + muvec b + deltavec c then mu, (lambda) / (2), delta are in? (A) AP (B) GP (C) HP (D) AGP

The vector vec x directed along the bisector of the angle between the vector vec a=7vec i-4vec j-4vec k and vec b=-2vec i-vec j+2vec k if |x|=45 is

if the vectors vec a=vec i+vec j+vec k, , b=vec i-vec j+2vec k and vec c=xvec i+(x-2)vec j-vec k are coplanar then x is