What is the dipole moment of BF3
The dipole moment μ describes the asymmetry of the charge distribution in the molecule as a measurable quantity.
μ is defined as "charge x distance". Is measurable μ (more precisely the amount of μ) from the evaluation of physical measurements (dielectric constant and refractive index). For qualitative considerations it is only important that μ is a quantity with magnitude and direction is.
μ is usually still in the unit D (1 D = 3.34 x 10^{30} C m). D = "Debye" after the Dutch physicist Peter Debye.
Graphically we symbolize μ with a arrow the from the positive to the negative charge shows. The length of the arrow corresponds to the Amount of μ. 

In Molecules the entire asymmetry of the charge distribution can be expressed as "geometric sum" the Asymmetry in the individual bonds are formed. (Total dipole moment = sum of bond dipole moments). For the "geometric sum", the arrows are added, taking into account the amount and the direction. In physics, this construction is known as the "force parallelogram". Mathematically, this construction is called a "vector addition". You can quickly understand this with examples.
Example 1: CO_{2}  linear molecule
O is more electronegative than C. 

Because of the opposite direction, the two individual moments cancel each other out, overall that has linear symmetric molecule CO_{2}no dipole moment (μ = 0). 

If two people of equal strength pull on a rope in exactly the opposite direction, the forces cancel each other out  and nothing happens. 

Example 2: H_{2}O  angled molecule
O is more electronegative than H. 

The two individual moments are added: 

The angled molecule H_{2}O Has a dipole moment (μ > 0). 

Example 3: BF_{3}  trigonal plane molecule (central atom + 3 equal partners in one plane)
F is more electronegative than B. 

The three individual moments are added: 

The trigonal plane molecule BF_{3}Has no dipole moment (μ = 0). 

Example 4: NH_{4}^{+}  Tetrahedral structure (central atom + 4 equal partners in tetrahedral environment)
N is more electronegative than H. 

The addition of the four individual moments yields the sum 0. 

Please provide a sketch of the "geometric sum" in a tetrahedron!  
Mathematical solution for "just trigonal":  
Mathematical solution for "tetrahedral": 
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