(1)|a| = √2let c=(x,y)=> x^2 +y^2 =2 (1)a.c =0(1,1)(x,y) =0=> x+y = 0(2)b.c >0(1,0)(x,y)>0=> x > 0sub (2) into (1)2x^2 = 2x = 1or-1( rejected , x>0)y = -1c ( 1,-1)(2)f...