# Unit Vector Question. *updated*

• imapeiceofwod
In summary, the problem presented is about finding the magnitudes of the forces exerted at point B by the cables AB and BC, given the total force exerted on B by the sailboat's forestay and backstay. The person asking for help has drawn a diagram and calculated the forces Fab=(4i,11.8j) and Fbc=(5i,-12j), and has found the total force in the i direction to be 9i and in the j direction to be 0.2j. However, the total force in the i direction should be 180i, which is causing confusion. They have also provided a picture of the situation, but the force vector acting on B is not shown.
imapeiceofwod
OK here's the problem. I am completely unsure how to solve it my teacher never even did an example like this before.

The total force exerted on the top of the mast B by the sailboat's forestay AB and backstay BC is 180i- 820j (N). What are the magnitudes of the forces exerted at B by the cables AB and BC?

A(0,1.2)
B(4,13)
C(9,1)

Any help please and thank you

here's what i got so far. I drew i diagram of the situation drawing and drew the vectors. I figured out Fab=(4i,11.8j) and Fbc=(5i,-12j)

Then i found the total force in the i direction which is 9i and the total force in the j which is 0.2j .

I know that the total force in the i direction is suppose to be 180i but i got 9i for the total force. Any help?

Since you have to achieve 180i- 820j (N) it seems rather odd your vectors are (4i,11.8j) +(5i,-12j).

Would you mind showing us the drawing with the vectors and the backstay/forestay ?

heres the picture

#### Attachments

• boat.png
4.8 KB · Views: 404
Ok, but I don't see the force vector acting on B.

AB and BC are basically ropes, so they're pulling or pushing B ? (I ask this looking at how you drew the arrows)

im sry, i drew the vector CB its suppose to be BC

don't mind, but draw the vector of the total force on B ...

## 1. What is a unit vector?

A unit vector is a vector with a magnitude of 1. It is often used in mathematics and physics to represent a direction or orientation.

## 2. How do you find the unit vector of a given vector?

To find the unit vector of a given vector, divide the vector by its magnitude. This will result in a vector with the same direction, but a magnitude of 1.

## 3. What is the importance of unit vectors in vector operations?

Unit vectors are important in vector operations because they allow us to easily represent and manipulate directions and orientations without having to consider the magnitude of the vector.

## 4. Can a zero vector be a unit vector?

No, a zero vector, which has a magnitude of 0, cannot be a unit vector because a unit vector by definition must have a magnitude of 1.

## 5. How are unit vectors represented in Cartesian coordinate systems?

In Cartesian coordinate systems, unit vectors are typically represented as i, j, and k for the x, y, and z directions, respectively. They are often written with a hat (^) symbol above to denote that they have a magnitude of 1.

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