if `vec b=2 vec i + 3 vec j - vec k` and `vec c= vec i + 4 vec j + 5 veck` then find a vector `vec a` such that `vec b * vec a =0` and `vec c * vec a=0`. Also find the unit vector along `vec a`.

If vec a = 2vec i + 2vec j + vec kvec b = 5vec i + vec j + 2vec k then | vec a xxvec b | ^ (2) + (vec a * vec b) ^ (2) =

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

vec a=2vec i+3vec j-vec k,vec b=-vec i+2vec j-4vec k and vec c=vec i+vec j+vec k then find thevalue of (vec a xxvec b)*(vec a xxvec c)

If vec a = i + j + k & vec b = i-2j + k, then the vector vec c such that vec a * vec c = 2 & vec a xxvec c = vec b is

If vec a=hat i+hat j+hat k and vec b=hat j-hat k, find a vector vec c such that vec a x vec c=vec b and vec a*vec c=3

vec a = vec i + 2vec j + 3vec k, vec b = -vec i + 2vec j + vec k, rArr3vec i + vec j and vec d is normal to both vec a and vec b then (vec c, vec d)

If a=vec i+4vec j,vec b=2vec i-3vec j and vec c=5vec i+9vec j then vec c=

If vec a = vec i + vec j + vec k, vec b = vec i - vec j + vec k and vec c = vec i + 2vec j - vec k, then the value of | [vec a.vec a, vec a.vec b, vec a.vec c], [vec b.vec a, vec b.vec b, vec b.vec c], [vec c.vec a, vec c.vec b, vec c.vec c ] | is equal to: (1) 2 (2) 4 (3) 16 (4) 64

If vec a = 2vec i-3vec j + vec k and vec b = -vec i + vec kvec c = 2vec j-vec k then the area of the parallelogram is having diagonals vec a + vec b and vec b + vec c is

The position vectors of the points A and B are vec i + 2 vec j + 3 vec k and 2 vec i - vec j - vec k respectively. Find the projection of vec (AB) on the vector vec i + vec j + vec k . Also find the resolved part of vec (AB) in that direction.