If `vec P` equal to `2i + 3j - k` and `vec Q` equal to `2i -5j+ 2k` find `vec P + vec Q` and `3vec P - 2 vecQ`

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

Let vec a = 2i + j + k, vec b = i + 2j + k and vec c = 2i-3j + 4k, A vector vec r satisfying vec r xxvec b = vec c xxvec b and vec r * vec a = 0 , is

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 .

Vector of length of 3 unit which is perpendicular to vec i + vec j + vec k and lies in the plane of vec i + vec j + vec k and 2vec i-3vec j, is (1) (3) / (sqrt ( 6)) (vec i-2vec j + vec k) (2) (3) / (sqrt (6)) (2vec i-vec j-vec k) (3) (3) / (sqrt (114)) ( 8vec i-7vec j-vec k) (4) (3) / (sqrt (114)) (- 7vec i + 8vec j-vec k)

Let vec a= hat j- hat k and vec c= hat i- hat j- hat k . Then vector vec b satisfying vec axx vec b+ vec c= vec0 and vec adot vec b=3 is (1) 2 vec i- vec j+2 vec k (2) hat i- hat j-2 hat k (3) hat i+j-2 hat k (4) - hat i+ hat j-2 hat k

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 p=5hat i+lambdahat j-3hat k and vec q=hat i+3hat j-5hat k then find the value of lambda such that vec p+vec q and vec p-vec q are perpendicular vectors.

Prove that the vectors 3 vec I + 5 vec j + 2 vec k, 2 vec I - 3 vec j - 5 vec k and 5 vec I + 2 vec j -3 vec k form the sides of an equilatera, triangle.

If vec(A) = 2 I + j - k , vec(B) = I + 2 j + 3 k , and vec(C ) = 6 i - 2 j - 6 k ,then the angle between (vec(A) + vec(B)) and vec(C ) will be