Column I, Column II Collinear vectors, p.` vec a` Coinitial vectors, q. ` vec b` Equal vectors, r. ` vec c` Unlike vectors (same intitial point), s. ` vec d`

Two vectors vec P and vec Q

If vec a is a unit vector, vec a xxvec r = vec b, vec a * vec r = c, vec a * vec b = 0 then vec r is equal to

If vec a is a unit vector, vec a xxvec r = vec b, vec a * vec r = c, vec a * vec b = 0, then vec r is equal to

Find the angle between the vectors vec a = 2 vec p + 4 vec q and vec b = vec p- vec q where vec p and vec q are unit vectors forming an angle of 120^@ .

If vec a and vec b are orthogonal unit vectors, then for a vector vec r noncoplanar with vec a and vec b , vector rxxa is equal to a. [ vec r vec a vec b] vec b-( vec r. vec b)( vec bxx vec a) b. [ vec r vec a vec b]( vec a+ vec b) c. [ vec r vec a vec b] vec a-( vec r. vec a) vec axx vec b d. none of these

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 ?

If vec P and vec Q are two vectors, then the value of (vec P + vec Q) xx (vec P - vec Q) is

Suppose that vec p, vec q and vec r are three non-coplanar vectors in R^3. Let the components of a vector vec s along vec p, vec q and vec r be 4, 3 and 5, respectively. If the components of this vector vec s along (-vec p+vec q +vec r), (vec p-vec q+vec r) and (-vec p-vec q+vec r) are x, y and z, respectively, then the value of 2vec x+vec y+vec z is

Find the vector a which is collinear with the vector vec b=2hat i-hat j and vec a*vec b=10