Vector Projections on the xy Plane and z Axis

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SUMMARY

The discussion focuses on vector projections in three-dimensional space, specifically on the xy plane and the z axis. The vector u has a length of 6 and forms a 40-degree angle with the z axis, while its projection on the xy plane makes a 44-degree angle with the x axis. The second vector v has a projection length of 5 on the z axis and a projection length of 6 on the xy plane, making a 136-degree angle with the x axis. The confusion arises from interpreting the angle measurements and their implications for vector components.

PREREQUISITES
  • Understanding of vector projections in three-dimensional space
  • Familiarity with trigonometric functions, specifically cosine and sine
  • Knowledge of vector notation and component representation
  • Basic principles of angles in relation to coordinate axes
NEXT STEPS
  • Study vector projection formulas and their applications in physics
  • Learn about trigonometric identities and their use in vector calculations
  • Explore three-dimensional coordinate systems and their geometric interpretations
  • Practice solving problems involving angles and lengths of vector projections
USEFUL FOR

Students studying physics or mathematics, particularly those focusing on vector analysis and projections in three-dimensional space.

DarkSamurai
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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>
 
Physics news on Phys.org
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?
 

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