If ` c` is a given non-zero scalar, and ` vec A` and `vec(B) ` are given non-zero vector such that ` vec A_|_ vecB ,` then find vector ` vec X` which satisfies the equation ` vec Adot vec X =c and vec Axx vec X= vec Bdot`

If vec b is not perpendicular to vec c , then find the vector vec r satisfying the equyation vec rxx vec b= vec axx vec b and vec r. vec c=0.

If vec a , vec b ,a n d vec c are non-zero vectors such that vec a. vec b= vec a. vec c , then find the geometrical relation between the vectors.

If vec(a) is a vector and x is a non-zero scalar, then

If vec a= hat i+ hat j+ hat k ,\ vec c= hat j- hat k are given vectors, then find vector vec b satisying the equation vec axx vec b= vec c\ a n d\ vec adot vec b=3.

If vec a , vec b ,a n d vec c are unit vectors such that vec a+ vec b+ vec c=0, then find the value of vec adot vec b+ vec bdot vec c+ vec cdot vec adot

If vec a and vec b are two given vectors and k is any scalar, then find the vector vec r satisfying vec rxx vec a+k vec r= vec b .

If vec a ,\ vec b ,\ vec c are unit vectors such that vec a+ vec b+ vec c= vec0 find the value of vec adot vec b+ vec bdot vec c+ vec cdot vec adot'

If vec a is perpendicular to vec b and vec r is non-zero vector such that p vec r+( vec rdot vec a) vec b= vec c , then vec r= vec c/p-(( vec adot vec c) vec b)/(p^2) (b) vec a/p-(( vec cdot vec b) vec a)/(p^2) vec a/p-(( vec adot vec b) vec c)/(p^2) (d) vec c/(p^2)-(( vec adot vec c) vec b)/p

If vec(A),vec(B) & vec(A)+vec(B) are three non - zero vector. Such that vec(A)+vec(B) is perpendicular to vec(B) then which of one is correct :

If vec(A) and vec(B) are two non - zero vectors such that |vec(A)+vec(B)|=(|vec(A)-vec(B)|)/(2) and |vec(A)|=2|vec(B)| then the angle between vec(A) and vec(B) is :