The values of k, for which `|k vec a| lt |vec a|` and `k vec a =1/2 vec a` is parallel to `vec a` hold true, lie in...

If |vec a|=8, |vec b|=3 and |vec axx vec b|=12 , then the value of vec a . vec b is

If for a vector vec a , vec a*hat i = vec a*hat j= vec a*hat k=0 , then find |vec a| .

Vectors vec a , vec b , vec c and vec d are given by vec a= hat i+ hat j+ hat k , vec b= 2 hat i+ 3 hat j , vec c= 3 hat i+ 5 hat j- 2 hat k and vec d= - hat j+ hat k . Show that the vectors vec b- vec a and vec d- vec c are parallel and find the ratio of their lengths.

If vec a = vec b , is it true that |quad vec a|=|quad vec b| ?

If vec axx vec b= vec cxxvec d and vec axx vec c= vec bxxvec d , show that vec a- vec d is parallel to vec b- vec c where vec a != vec d , vec b != vec c .

What is the value of [vec a vec b vec c] if vec a, vec b, vec c are non-zero coplanar vectors ?

If vec a and vec b are two vectors such that |quad vec a|=2 , |quad vec b|=1 and vec a. vec b=1 , then find the value of (3 vec a - 5 vec b).(2 vec a+7 vec b) .

Prove that [vec a+ vec b, vec b +vec c, vec c + vec a]= 2 [vec a vec b vec c]

If vec alpha=3 hat i-hat j and beta=2 hat i+hat j-3 hat k , express vec beta in the form vec beta=vec (beta)_1+ vec (beta)_2 where beta_1 is parallel to vec alpha and vec(beta)_2 is perpendicular to vec alpha .

If vec a , vec b and vec c are three vectors such that vec a+vec b+vec c=vec 0 , |quad vec a|=1 , |quad vec b|=4 and |quad vec c|=2 , then find the value of vec a.vec b+vec b.vec c+vec c.vec a .