In the figure, \( \overrightarrow{O A}=\vec{a}, \overrightarrow{O B}=\vec{b} \) and \( \overrightarrow{A B}=2 \overrightarrow{A P} \), find the value of \( \overrightarrow{O P} \) in terms of \( \vec{a} \) and \( \vec{b} \).

In \( \triangle \mathrm{TUV}, u=750 \mathrm{~cm}, v=670 \mathrm{~cm} \) and \( \angle \mathrm{T}=160^{\circ} \). Find the length of \( t \), to the nearest centimeter.

In \( \triangle \mathrm{EFG}, e=880 \) inches, \( f=140 \) inches and \( g=890 \) inches. Find the measure of \( \angle \mathrm{G} \) to the nearest 10th of a degree.

In \( \triangle \mathrm{TUV}, u=4.8 \mathrm{~cm}, v=4.4 \mathrm{~cm} \) and \( \angle \mathrm{T}=84^{\circ} \). Find the length of \( t \), to the nearest 1oth of a centimeter.

In \( \triangle \mathrm{NOP}, n=54 \) inches, \( o=97 \) inches and \( p=95 \) inches. Find the measure of \( \angle \mathrm{N} \) to the nearest degree.

In \( \triangle \mathrm{EFG}, e=96 \mathrm{~cm}, f=71 \mathrm{~cm} \) and \( \angle \mathrm{G}=52^{\circ} \). Find the length of \( g \), to the nearest centimeter.