Can you prove ?
If yes, then read further else skip this note.
Do you know what is 'Scalar Product of two vectors'?
- Scalar product of two vectors: For vectors and , the scalar product is defined by where is the angle, in radians with between and . This is a scalar quantity; that is, a real number, not a vector. The scalar product has the following property:
Now, the climax:
If and are two vectors having an angle between them[ being the smaller angle]
The magnitude of the sum of two vectors is written as
using (1), equation (2) can be written as
. TaDa! This is the expression for the magnitude of sum of two vectors. Same thing can be derived geometrically.You can find the geometric prove in any standard textbooks.
I found this when I was confused whether 2 is the coefficient of or not. More significant is the message that symbolic notation in Mathematics is not just to threaten students. Sometimes they help us understand things in simple shorter ways.
Have you ever exploited symbolic notation of Mathematics? Share an example.
[Try to be as elementary as possible]