The force on an object is F = -10j. For the vector v = -i + j, find...?

(a) The unit vector along v is
n=(-i+j)/sqrt(2) and the component
of F parallel to v is
Fn=F*n=-10j*(-i+j)sqrt(2)=-5sqrt(2)n

(b) Let this component be Fn', then
Fn+Fn'=-10j=>
Fn'=-10j-[-5sqrt(2)n]=>
Fn'=-10j+5sqrt(2)n=>
Fn'=-5i-5j

(c) | v|=|-i+j|=sqrt(2)
W=F*v=-10j*(-i+j)=-10

so which you get the displacement as d = (6-8)i + (0 - 8)j + (-a million +8)ok = -2i - 8j + 7k So the artwork executed is given through W = f . d = (10i + 10j + 7k) . ( -2i -8j + 7k) = -20 - eighty + 40 9 = -51