Prove that  is orthogonal to , for any vectors 

Prove that

if and only if  are orthogonal.

Let  be the two non-zero vectors. Then, prove that  are perpendicular if and only if 

Prove that two vectors  are perpendicular if 
       

If  are perpendicular, then 
 

If  such that each is perpendicular to sum of the other two, find 

167.

Find  if two vectors  are such that 

Find  if 

Find  if 

If  are unit vectors, and  is the angle between them, find  in terms of .