Step 1: Understand dipole moment concept.
Dipole moment depends on molecular geometry and polarity of bonds. It is a vector quantity, so resultant dipole depends on both bond polarity and symmetry of the molecule. Symmetrical molecules have zero dipole moment, while asymmetrical molecules have non-zero values.
Step 2: Analyze BF\(_3\).
BF\(_3\) has trigonal planar geometry with three identical B–F bonds arranged symmetrically at 120°. The individual bond dipoles cancel each other completely due to symmetry, giving:
\[
\mu = 0
\]
So BF\(_3\) has the smallest dipole moment.
Step 3: Analyze NF\(_3\).
NF\(_3\) has trigonal pyramidal geometry due to lone pair on nitrogen. Although N–F bonds are polar, fluorine is highly electronegative, and bond dipoles partially oppose the lone pair effect, resulting in a small net dipole moment. Hence NF\(_3\) has a low but non-zero dipole moment.
Step 4: Analyze NH\(_3\).
NH\(_3\) also has trigonal pyramidal geometry with a lone pair on nitrogen. N–H bonds are polar and their dipoles reinforce the lone pair effect rather than cancel it. Therefore, NH\(_3\) has a comparatively larger dipole moment than NF\(_3\).
Step 5: Compare all molecules.
From analysis:
\[
BF_3 = 0 \lt NF_3 \lt NH_3
\]
Thus, dipole moment increases in the order:
\[
BF_3 \lt NF_3 \lt NH_3
\]
Step 6: Final conclusion.
Therefore, the correct order of dipole moments is:
\[
\boxed{BF_3 \lt NF_3 \lt NH_3}
\]