Find the components of a unit vector

In summary, the problem involves finding the angle that bar AB makes with the horizontal, using basic geometry, similar triangles, and the Pythagorean Theorem. The suggested approach is to draw a line from the origin to point B and use the law of cosines to determine the angle.
  • #1
seanster1324
8
0

Homework Statement



http://i.imgur.com/B1hFY6E.png

Homework Equations



-Basic geometry
-Similar triangles (?)
-Pythagorean Theorem

The Attempt at a Solution



-I need to find the angle the bar AB makes with the horizontal, correct? And with that, I will be able to figure out the components for the unit vector...
-I'm stuck at where exactly to start. I feel as though there are generalizations I am not making that are necessary to begin...
 
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  • #2
Draw a picture of the curved bar and lay out the straight bar as shown on the diagram. Can you figure out the components of the vector AB? Remember the length of AB is given.
 
  • #3
seanster1324 said:

Homework Statement



http://i.imgur.com/B1hFY6E.png

Homework Equations



-Basic geometry
-Similar triangles (?)
-Pythagorean Theorem

The Attempt at a Solution



-I need to find the angle the bar AB makes with the horizontal, correct? And with that, I will be able to figure out the components for the unit vector...
-I'm stuck at where exactly to start. I feel as though there are generalizations I am not making that are necessary to begin...

Draw a line from the origin to B. You know this distance, right? So you have all 3 sides of a triangle & from that you can determine your angle using law of cosines.
 

Related to Find the components of a unit vector

1. What is a unit vector?

A unit vector is a vector with a magnitude of 1. This means that it has a length of 1 and is used to indicate direction.

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

To find the components of a unit vector, you first need to find the magnitude of the original vector. Then, divide each component of the vector by the magnitude to get the unit vector components.

3. Why is it important to find the components of a unit vector?

Finding the components of a unit vector is important because it allows you to represent a vector in terms of its direction and magnitude. This is useful in many applications, such as physics and engineering.

4. Can the components of a unit vector be negative?

No, the components of a unit vector cannot be negative. A unit vector always has a magnitude of 1, which means that its components must be positive.

5. How do you use unit vectors in real life applications?

Unit vectors are used in many real life applications, such as calculating forces in physics or representing directions in navigation. They are also used in computer graphics to represent transformations and rotations in 3D space.

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