Example: 1  
From any two vectors and , prove that
When does the equality hold in these cases?

Solution: 1  
Consider this figure:
The first two relations follow from the fact that in any triangle, the sum of two sides is greater than the third side:
In
In
In the first relation, the equality can hold only if the two vectors have the same direction; this should be intuitively obvious:
The equality in the second relation holds if the two vectors are exactly opposite
To prove the third relation, we use in in Fig , the geometrical fact that the difference of any two sides of a triangle is less than its third side:
The equality holds when and are precisely in the opposite direction
The main point to understand from this example is how easily vector relations follows from corresponding geometrical facts
