Find the x, y, and z components of the vector

In summary, the x, y, and z components of the vector A shown in the figure are 57.54m, 30.70m, and 37.28m respectively. The x and y components were found by using the component of A on the x-y plane, which makes an angle of 35 degrees with the x-axis. The x and y components can be calculated using the formula 65m*cos(35)*cos(35) and 65m*cos(35)*sin(35).
  • #1
Flippit
9
0

Homework Statement


Find the x, y, and z components of the vector A shown in the figure , given that A = 65 m.

A link to the image: http://img401.imageshack.us/i/asdasp.jpg/

The Attempt at a Solution



Y Component: 65m*cos(35) = 53.24m

Z Component: 65m*cos(55) = 37.28m

I think these two are right, but I don't have a clue how to solve for the X component.
 
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  • #2
Your Z component is correct.
The other component 65m*cos(35) the component of A on the x-y plane.
From this component find the x and y components.
 
  • #3
rl.bhat said:
Your Z component is correct.
The other component 65m*cos(35) the component of A on the x-y plane.
From this component find the x and y components.

Do you think you could give me just a little nudge in the right direction? I can't figure out how to go from here.
 
  • #4
65m*cos(35) is the component of A on the x-y plane.
This component makes 35 degrees with the x-axis.
Hence its component on x-axis is 65m*cos(35)*cos(35)
and on y-axis is 65m*cos(35)*sin(35)
 
  • #5
Okay, I understand everything now, thanks so much for the help!
 

1. What is a vector?

A vector is a mathematical object that has both magnitude (size) and direction. It is commonly represented as an arrow in a coordinate system, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction.

2. What are the x, y, and z components of a vector?

The x, y, and z components of a vector refer to the values of the vector in each of the three dimensions of a Cartesian coordinate system. The x-component is the value of the vector along the x-axis, the y-component is the value along the y-axis, and the z-component is the value along the z-axis.

3. How do you find the x, y, and z components of a vector?

To find the x, y, and z components of a vector, you can use trigonometric functions and the magnitude and direction of the vector. For example, if you know the magnitude and angle of the vector, you can use cosine and sine to find the x and y components, respectively. The z-component can be found using the Pythagorean theorem.

4. Why is it important to find the x, y, and z components of a vector?

Finding the x, y, and z components of a vector is important because it allows us to break down a vector into its individual parts and better understand its overall direction and magnitude. This can be especially useful in physics and engineering applications, where vectors are commonly used to represent forces and velocities.

5. Can you find the x, y, and z components of a vector in any coordinate system?

Yes, you can find the x, y, and z components of a vector in any coordinate system, as long as you know how to convert between coordinate systems. The process for finding the components may vary slightly depending on the coordinate system, but the principles remain the same.

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