The pth, qth and rth terms of a GP are the positive numbers a,b and c respectively. Show that the vectors ` vec i log_e a + vec j log _e b + vec k log _e c` and `vec i (q-r) + vec j (r-p) + vec k (p-q)` are mutually perpendicular.

Prove that vector vec i-2vec j+5vec k and -2vec i+4vec j+2vec k are mutually Is perpendicular|

The vectors vec(A)=ai-3j+k and vec(B)=i+j+k are mutually perpendicular.Then value of a 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 .

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

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= hat i+ hat j+ hat k , vec c= hat j- hat k , vec adot vec b=3 and vec ax vec b= vec c , then vec b is equal to

The position vectors of P and Q are respectively vec a and vec b . If R is a point on vec(PQ) such that vec(PR) = 5 vec(PQ), then the position vector of R, 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

Consider the three vectors p,q, and r such that vec p=vec i+vec j+vec k and vec q=vec i-vec j+vec k;p xx r=q+cp and p.r=2

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