Position of paul with respect to john is given as
14 m due west of john
[tex]r_{pj} = r_p - r_j = -14\hat i[/tex]
position of George with respect to Paul is given as 36 m in direction 37 degree south of east
[tex]r_{GP} = r_G - r_p = 36cos37\hat i - 36 sin37\hat j[/tex]
now we need to find the position of George with respect to John
[tex]r_{GJ} = r_G - r_j[\tex]
now for the above equation we can add the two equations
[tex]r_{Gj} = -14\hat i + 36 cos37\hat i - 36sin37\hat j[/tex]
[tex]r_{Gj} = 14.75\hat i - 21.67\hat j[/tex]
so the magnitude is given as
[tex]r = \sqrt{14.75^2 + 21.67^2} = 26.2 m[/tex]
and direction is given as
[tex]\theta = tan^{-1}\frac{21.67}{14.75}= 55.75 degree[/tex]
so it is 26.2 m at an angle 55.75 degree South of east
