we know the length of the cable is 9m.
That means the magnitude of rAB=9m.
The unit vector, denoted u, is each of rAB divided by the magnitude.
u=(x/9i−y/9j−z/9k)
We can also figure out the unit vector of F.
u=(350i - 250j - 450k)/√(350² +(-250)² +(-450)²)
u=0.562i−0.401j−0.723k
Force F is directed from point A to B, then both unit vectors must be equal.
Therefore
(x/9i−y/9j−z/9k)=0.562i−0.401j−0.723k
We can now solve for each term
x/9=0.562----- > x=5.058 m
-y/9=-0.401--------- > y=3.609 m
-z/9=-0.723------- > z=6.507 m
The answer is
the coordinates of point a
(5.058,3.609,6.507)
