# Static Case Study for dot product

1. Oct 12, 2008

### ricky_fusion

1. The problem statement, all variables and given/known data
* With an axis system oriented as shown, the position vectors of points A and B are
rA = 175i + 0j + 0k m
rB = 39i + 70j + 29k m

* When the trolley is halfway between points A and B, the forces exerted on the trolley by the cables are
F1 = -943.7i - 221.7j + 245.4k m
F2 = -919.4i - 216.0j - 328.6k m
What is the component of the force exerted on the trolley that is parallel to the line AB?

For detail : https://ecourses.ou.edu/cgi-bin/ebook.cgi?doc=&topic=st&chap_sec=02.4&page=case_intro

2. Relevant equations

The dot product of two vectors A and B is defined as the product of the magnitudes A and B and the cosine of the angle θ between them:

A • B = |A| |B| cosθ

The dot product can also be calculated by

A • B = Ax Bx + Ay By + Az Bz
Using the dot product, the angle between two known vectors A and B, can be determined as

θ = cos^-1 AB/AB

If the direction of a line is defined by the unit vector u, then the scalar component of the vector A parallel to that line is given by

A|| = A • u

The vector component parallel to that line is given by

A|| = (A • u) u

For Detail : https://ecourses.ou.edu/cgi-bin/ebook.cgi?doc=&topic=st&chap_sec=02.4&page=theory

3. The attempt at a solution
The scalar component of the total force parallel to the direction uAB can be found by using the dot product,

FT|| = FT • uAB

= -1,863 (-0.8736) - 437.7 (0.4496) - 83.2 (0.1863)

= 1,415 N

Multiply the scalar component by the unit vector uAB to determine the vector component parallel to the line AB:

FT|| = FT • uAB

= -1,236i + 636.3j + 263.7k N

= 1,415 N

For detail : https://ecourses.ou.edu/cgi-bin/ebook.cgi?doc=&topic=st&chap_sec=02.4&page=case_sol

My question
How is to find out the 1,415 N for scalar component and multiply scalar component??

Thnks,
Ricky
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution