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## Homework Statement

This is an example problem in my calculus textbook. I don't get how they relate the position vector to the force vector. I have taken a calculus based physics course and I don't remember establishing such relationship between the position and the force vectors.

Note: I have attached a picture of the situation.

[/B]

A television camera weighing 120 pounds is supported by a tripod, as shown in Figure 11.23. Represent the force exerted on each leg of the tripod as a vector.

## Homework Equations

u=

*c*v

v + u= v1 + u1, v2 + u2, v3 + u3

cv=cv1, cv2, cv3

3. The Attempt at a Solution

Let the vectors and represent the forces exerted on the three legs. From Figure 11.23, you can determine the directions of and to be as follows:[/B]

**PQ1= <0,-1,-4>**

PQ2= <√3/2, 1/2,-4>

PQ3= <-√3/2, 1/2,-4>

PQ2= <√3/2, 1/2,-4>

PQ3= <-√3/2, 1/2,-4>

**Because each leg has the same length, and the total force is distributed equally among the three legs, you know that the magnitude of F1=F2=F3. So, there exists a constant such that**

**F1=**

*c*

**<0,-1,-4>=F2=**

*c*

**<√3/2, 1/2,-4>=F3=**

*c*

**<-√3/2, 1/2,-4>**

Let the total force exerted by the object be given by F= <0,0,-120> Then, using the fact that

F= F1 + F2 + F3

Let the total force exerted by the object be given by F= <0,0,-120> Then, using the fact that

F= F1 + F2 + F3

you can conclude that

**F1, F2, and F3 all have a vertical component of -40. This implies that**

*c*

**(-4)= -40 and**

*c*

**is equal to 10.**

Therefore, the forces exerted on the legs can be represented by

F1= <0,- 10, -40>

F2= <5√3, 5, -40>

F3=

Therefore, the forces exerted on the legs can be represented by

F1= <0,- 10, -40>

F2= <5√3, 5, -40>

F3=

**<-5√3, 5, -40>**
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