Vector Projections on the xy Plane and z Axis

In summary, the given conversation discusses two vectors, u and v, and their respective vector projections on the z axis and xy plane. The vector u has a length of 6 and makes an angle of 40 degrees with the z axis, while its vector projection on the xy plane has a length of 5 and an angle of 44 degrees with the x axis. The vector v has a length of 5 as its projection on the z axis, and a length of 6 and an angle of 136 degrees as its projection on the xy plane. The wording of the problem may be confusing, but the solution involves finding the magnitude and cosine of the angle in each case.
  • #1
DarkSamurai
7
0

Homework Statement


The vector u of length 6 makes an angle of 40 with the z axis; it's vector projection on the xy plane makes an angle of 44 degrees with the x axis.

The vector projection of a second vector v on the z axis has a length 5. The vector projection of v on the xy plane has a length of 6 and makes an angle of 136 with the x axis.

Homework Equations


u = <i, j, k>
v = <i, j, k>

The Attempt at a Solution


im confused on the wording of the problem but this is how I see it...

<5cos(44),0,5sin(40)>
<5cos(136), 0, 6>
 
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  • #2
The first part confuses me, "length x makes an angle of theta with the z axis"

What does this mean? on the zx plane? So should I take the magnitude and then take the cos of the angle?
 

Related to Vector Projections on the xy Plane and z Axis

1. What are vectors u and v projections?

Vectors u and v projections are mathematical concepts used to find the component of a vector in a particular direction. They are often used in physics, engineering, and other sciences to analyze motion and forces.

2. How do you calculate the projection of a vector onto another vector?

The projection of a vector u onto another vector v can be calculated using the formula:
projvu = (u · v / |v|2) * v. This involves taking the dot product of the two vectors and dividing it by the magnitude of v squared, then multiplying it by v.

3. Can vectors u and v projections be negative?

Yes, vectors u and v projections can be negative. The sign of the projection indicates the direction of the component of the vector in relation to the direction of the other vector.

4. What is the difference between scalar and vector projections?

The scalar projection of a vector onto another vector is the magnitude of the projection, while the vector projection also includes the direction of the projection. The scalar projection is a scalar quantity, while the vector projection is a vector quantity.

5. How are vectors u and v projections used in real-world applications?

Vectors u and v projections are used in many fields, such as physics, engineering, and computer graphics. They are used to analyze forces, calculate work and energy, and simulate motion of objects in 2D and 3D space.

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