Finding magnitude and direction of vectors help

In summary, the conversation discusses the method of components for solving vector problems and how to find the magnitude and angle of a resultant vector. The use of trigonometry and the Pythagorean theorem are mentioned as tools for solving these types of problems. Additional resources are also provided for further understanding.
  • #1
Encarta
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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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  • #3
Thanks, that helped.
 

What is a vector?

A vector is a mathematical object that has both magnitude (size) and direction. It is represented by an arrow, with the length of the arrow indicating the magnitude and the direction of the arrow indicating the direction.

How do you find the magnitude of a vector?

The magnitude of a vector can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides. In the case of a vector, the hypotenuse is the magnitude and the other two sides represent the x and y components of the vector.

How do you find the direction of a vector?

The direction of a vector can be found by calculating the inverse tangent of the y component divided by the x component. This will give an angle in radians, which can then be converted to degrees if needed.

What is the difference between magnitude and direction?

Magnitude refers to the size of a vector, while direction refers to the angle at which the vector is pointing. Both are necessary to fully describe a vector.

Can vectors be negative?

Yes, vectors can have negative components. This indicates that the vector is pointing in the opposite direction of the positive component. However, the magnitude of a vector is always positive.

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