let b = ( m,n)
向量b在x軸上的投影為2
m = 2
b = (2,n)
a=(4,3)
向量a在向量b上的投影為5倍根號2/2
=> a.b /|b| = 5√2/2
(4,3).(2,n)/√(4+n^2) = 5√2/2
(8+3n)/√(4+n^2) = 5√2/2
2(8+3n)= 5√2√(4+n^2)
4(8+3n)^2 = 50(4+n^2)
14n^2-192n-56=0
7n^2 -96n - 28 =0
n = 14( rejected) or -2/7 (|b| < 14)
b = ( 2,-2/7)