Finding magnitude and direction of vectors help

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SUMMARY

The discussion focuses on solving a vector problem involving force vectors A and B, with magnitudes of 27 lb and 44 lb, respectively, at specified angles. The goal is to find vector C such that the equation 2A + C - B results in a vector with a magnitude of 38 lb pointing in the +x direction. Key equations utilized include the horizontal and vertical components of vectors and the Pythagorean Theorem. The user successfully calculated the components of vectors A and B but required further guidance on determining the magnitude and direction of vector C.

PREREQUISITES
  • Understanding of vector components and their calculations
  • Familiarity with trigonometric functions (sine, cosine, tangent)
  • Knowledge of the Pythagorean Theorem
  • Basic principles of vector addition and subtraction
NEXT STEPS
  • Study vector addition techniques in detail
  • Learn how to resolve vectors into components using trigonometric functions
  • Explore the concept of resultant vectors and their calculations
  • Practice solving similar vector problems using different magnitudes and angles
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Students in physics or engineering courses, educators teaching vector analysis, and anyone seeking to improve their understanding of vector addition and resolution techniques.

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Homework Statement



Given the following force vectors: A is 27 lb at an angle of 28° clockwise from the +x-axis, and B is 44 lb at an angle of 52° clockwise from the +y-axis.
(a) Using the method of components find the magnitude and angle of the vector C such that 2A + C − B results in a vector with a magnitude of 38 lb pointing in the +x direction.

Homework Equations


Horizontal component of a Vector A = A * cos [tex]\Phi[/tex]
Vertical Component of a Vector A = A* sin [tex]\Phi[/tex]
tan [tex]\Phi[/tex] = Vertical component of A/horizontal component of A
Pythagorean Theorem

The Attempt at a Solution


To solve this, I've calculated the x and y components of vectors A and B, but do not know where to go from here. The closest I could get to an answer was I drew the vectors in coordinate system and drew the resultant vector that was asked of me. But I have no idea how to proceed with finding the magnitude and the exact direction.
A, B, and C are vectors.
Thanks for explaining.
 
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Thanks, that helped.
 

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