Question 1097489
<br>I will assume -- since it makes your answers look reasonable -- that "R" is a unit vector to the "R"ight and "U" is a unit vector "U"p. Then your vector 4R-14U us the resultant vector of the Cartesian point (4,-14).  ("4 right and -14 up").<br>
Then the magnitude of the vector is
{{{sqrt(14^2+4^2) = sqrt(212) = 2*sqrt(53)}}}
which agrees with your answer.<br>
But the Cartesian point is in the 4th quadrant; your angle has the right components, but it is in the 2nd quadrant.  So the angle for your vector is exactly 180 degrees away from where it should be.<br>
Of course, all my comments are irrelevant if I have guessed wrong about the meanings of vectors R and U.