Vector Addition and Displacement Magnitude in 3D Space

In summary, the conversation discusses the components and magnitude of a displacement vector from a base camp to the summit of a mountain, measured on a map. The chosen axes are x-axis east, y-axis north, and z-axis up. The vector is represented by i + j + k and the coordinates are x=4580, y=2450, with a 32.4 degree west of north direction. The z-axis is located upwards, and the 2450 component is between the x and y axes.
  • #1
jared69sib
38
0

Homework Statement



The summit of a mountain, 2450m above the base camp, is measured on a map to be 4580m horizontally from the camp in a direction 32.4 degrees west of north. What are the components of the displacement vector from camp to summit? What is its magnitude? Choose the x-axis east, y-axis north, and z axis up.

Homework Equations



vector r = i + j + k

The Attempt at a Solution



I don't think I am drawing the diagram correctly. Not sure where to put z axis. I keep ending up with a triangle. x= 4580, y=2450, bottom angle 32.4...
 
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  • #2
hi jared69sib! :smile:

the z axis is up,

and the 2450 is between the x and y axes :wink:
 
  • #3
tiny-tim said:
hi jared69sib! :smile:

the z axis is up,

and the 2450 is between the x and y axes :wink:

Thank you. It was hard to visualize for the very first time.
 

1. What is vector addition?

Vector addition is the process of combining two or more vectors to find their resultant vector. It takes into account both the magnitude and direction of each vector to determine the overall magnitude and direction of the resultant vector.

2. How do you add vectors?

To add vectors, you first need to break them down into their components (x and y for 2D vectors). Then, you can add the x components together and the y components together. The resultant vector can then be found using the Pythagorean theorem to calculate the magnitude and trigonometry to determine the direction.

3. What is the difference between scalar and vector addition?

Scalar addition is the process of adding two or more quantities that only have magnitude, such as numbers. Vector addition, on the other hand, takes into account both magnitude and direction. This means that when adding vectors, the direction of each vector must also be considered in order to find the resultant vector.

4. Can vectors be added in any order?

Yes, vectors can be added in any order. This is because vector addition is commutative, meaning the order in which the vectors are added does not affect the final result. However, the direction of the resultant vector may be different depending on the order in which the vectors are added.

5. What is the importance of vector addition in physics?

Vector addition is important in physics because it is used to determine the overall forces acting on an object. By combining all the individual forces (vectors), we can find the net force, which is crucial in understanding the motion of an object. Vector addition is also used in other areas of physics, such as in calculating electric and magnetic fields.

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