Question
For any two vectors 
, prove that
(i) 
(ii) 
(iii) 
Solution
Case I, 
are non-collinear vectors.
Let
We know that in a triangle sum of two sides of triangle is always > third side
Case II.
are collinear vectors.
Let
are non-collinear vectors. Let
We know that in a triangle sum of two sides of triangle is always > third side
Case II.
are collinear vectors.Let
Also, 
Now,
Combining the results of Case I and II, we get,
Combining the results of Case I and II, we get,
(ii)
(iii)
Now,
Combining the results of Case I and II, we get,
Combining the results of Case I and II, we get,
(ii)
(iii)
