Question

If f = 350i - 250j - 450k6 n and cable ab is 9 m long, determine the x, y, z coordinates of point a

Answer 1

 we know the length of the cable is 9m.
That means the magnitude of  r​AB​​=9m.
The unit vector, denoted u, is each of r​AB​​ divided by the magnitude.

u=(​​​x/9​​i−​y/9​​j−​z/9​​k)

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/9​​i−​y/9​​j−​z/9​​k)=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)