A pole, 6 m long, lies along the x-axis with one end at the origin. A rope is attached to the other end (point A), which runs to a point on the wall (point B), given by the coordinates (0,-1,2) in meters. Also at point A, there is a force given by F = 400 i - 200 j + 500 k (in N). Determine the projected component of this force (in N) acting along the rope AB.

The value  is

Explanation:

From the question we are told that

   The length of the first rope is  L  =  6 m

    The first rope lie on the x-axis

   The end point of the first rope is  A  

   Now the vector of  A will be

   The point of the second rope on the wall is  B

   The coordinate for the point of the second rope on the wall is  (0,-1,2)

   The vector of B will be  

Now the coordinate of rope AB is mathematically represented as

=>  

=>  

Generally the magnitude of the rope AB is mathematically evaluated as

Generally the unit vector rope AB is mathematically evaluated as

=>    

From the question we are told that there is a force acting at point A and the force is  

Generally the projected component of this force (in N) acting along the rope AB is mathematically represented as

=>      

Note ( i . i = 1  ) , (j . j  = 1) , (k . k  = 1)

So    

=>  

So the magnitude of the projected component of this force (in N) acting along the rope AB is