What are the rules for expressing angles and finding vector components?

In summary: Then use the rule above. In summary, the rule is that if all angles in a problem are given with reference to the same direction (say with reference to north), you can use the given angles for finding the components. If the angles given are with reference to different direction (say one wrt north, another wrt west), then be careful.
  • #1
luxor106
1
0

Homework Statement



So I have been doing the adding of vectors by using their components and you are suppose to use the + X axis as a reference frame so when 3 vectors are given do you always have to subtract the given theta from the quardrant total ie. 22m, 56 degrees west of south plotting this places the vector with in the 3rd quadrant so you would have to do 270-56 in order to get the degree used in the vx= v cos theta or vy= vsin theta. but I have seen other problems where the vector resides in the 3rd quadrant and the solution is achieved by using the theta stated in the problem and you do not have to subtract it from the 270. So i am confused about the rules of the is process can someone please explain

Homework Equations



vx= v cos theta
vy= v sin theta

The Attempt at a Solution

 
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  • #2
yes your method is right,
but they might be right too, what they did can be correct if you take south to be the positive x-axis, but usually x-axis is east because we're used to it and you don't have to thing down is increasing and where would y be? O.O
 
  • #3
There are several methods for expressing an angle, all correct. For example : an angle 110 degrees north of east can also be expressed as 70 degrees north of west. cos110 deg = -0.34 and cos70 deg = 0.34. Thus, both ways of expressing the angle lead to same result except the sign.

You can follow the rule : If all angles in a problem are given with reference to the same direction (say with reference to north) then you can use the given angles for finding the components. Signs + or - will be automatically taken care. However, if the angles given are with reference to different direction (say one wrt north, another wrt west), then be careful. To avoid making a mistake you could convert all the given angles wrt to one reference (say north).
 

What is a vector?

A vector is a mathematical representation of a quantity that has both magnitude (size) and direction. It is typically represented by an arrow pointing in the direction of the vector, with the length of the arrow representing the magnitude of the vector.

How is a vector represented?

A vector is typically represented by its components, which are its magnitude in each axis. For example, a vector with a magnitude of 5 in the x direction and -3 in the y direction would be represented as (5, -3). Alternatively, it can also be represented by its magnitude and direction, using the notation |v|∠θ, where |v| is the magnitude and θ is the angle between the vector and the positive x-axis.

What is the relationship between a vector and the + x axis?

The + x axis is a reference direction that is often used to describe the direction of a vector. A vector that is parallel to the + x axis has a direction of 0 degrees or 180 degrees, depending on the direction of the positive x axis. A vector that is perpendicular to the + x axis has a direction of 90 degrees or 270 degrees.

How are vectors added and subtracted?

To add or subtract vectors, their components are added or subtracted separately. For example, to add two vectors (5, 2) and (-3, 4), we add their x components (5 + (-3) = 2) and their y components (2 + 4 = 6), resulting in a new vector (2, 6). This is known as the head-to-tail method of vector addition.

What is the difference between a position vector and a displacement vector?

A position vector represents the location of a point in space relative to a reference point, whereas a displacement vector represents the change in position of an object. Position vectors are usually fixed and do not change, while displacement vectors can change depending on the motion of the object.

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