# Finding position vectors of x y z in meters

• Sneakatone
In summary, the conversation discusses the use of altitude, horizontal distance, and bearing to describe the position of an aircraft relative to an airport. The question is posed about finding the x,y,z components of the position vector, with the x-axis being east, the y-axis being north, and the z-axis being vertical. There is a discussion about finding the y coordinate and using the Pythagorean theorem to solve for the x coordinate, with the understanding that the z coordinate is independent of the horizontal position. The conversation ends with a question about drawing a diagram to better understand the vector in the x-y plane.
Sneakatone
Air traffic controllers usually describe the position of an aircraft relative to the airport by altitude horizontal distance and bearing . suppose an air craft altitude 1450 m , distance 24 km , and bearing 18.0 degrees east of north. what are the x,y,z components in meters of the position vector? the x-axis is east the y-axis is north and the z axis is vertical.

I cannot seem to find the value for x

but I have solved for
y= 22550 m
z=1450 m

How did you get you y coordinate? If you know y and the distance, how would you find x?

I found y by subtracting 24000m by 1450m

Why do that? 1450 m is the altitude, the z coordinate. It is independent of the horizontal position. Draw a diagram of the x-y plane.

is this suppose to make a a triangle? i tried the pythagorean theorem but it dosent seem to work.

Did you draw the diagram?

You have a vector in the x-y plane with a specified length and direction. You want to find out the x and y coordinates. How do you do that?

## 1. What are position vectors in terms of x, y, and z?

Position vectors represent the location of a point in three-dimensional space, using the coordinates x, y, and z as its components.

## 2. How do you find the position vector of a point in meters?

To find the position vector in meters, you must first determine the x, y, and z coordinates of the point. Then, you can create a vector with these coordinates as its components, with the unit of measurement being meters.

## 3. Can position vectors be negative?

Yes, position vectors can have negative components. This indicates that the point is located in the negative direction of the corresponding axis.

## 4. How do you calculate the magnitude of a position vector?

The magnitude of a position vector is calculated using the Pythagorean theorem, by taking the square root of the sum of the squares of its components. This represents the distance between the point and the origin.

## 5. What is the significance of position vectors in scientific research?

Position vectors play a crucial role in scientific research, particularly in fields such as physics, engineering, and astronomy. They allow for precise and accurate measurements of the location of objects in three-dimensional space, which is essential for understanding and predicting their behavior.

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