Angle Vector Problem

In summary: I think i understand now!In summary, the sum of the four vectors in unit-vector notation is (-3.18m)i + (4.73m)j, with a magnitude of 5.70 m and an angle of -56.09 degrees (or 123.91 degrees when adjusted for quadrant). The confusion may have been due to the calculator giving an angle in the opposite direction, which can be resolved by adding 180 degrees to the answer.
  • #1
What is the sum of the following four vectors in (a) unit-vector notation, and as (b) a magnitude and (c) an angle? Positive angles are counterclockwise from the positive direction of the x axis; negative angles are clockwise.

http://edugen.wiley.com/edugen/courses/crs1650/art/qb/qu/c03/eq03_84.gif

My Answers:

a) (-3.18m)i + (4.73m)j
b) 5.70 m
c) -56.09 degrees

Part C was marked wrong and I don't understand why... i did tan inverse of (4.73/-3.18) to get my answer. Could someone tell me what I did wrong?
 
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  • #2
Hi goaliejoe35,

If you draw a set of x- and y- axes on a paper and draw the vector that you gave in part a, what quadrant is it in? What quadrant is the angle the you put as the answer to part c in?
 
  • #3
the vector from part a is in quadrant 2 right? and the angle i gave is in quadrant 4?
 
  • #4
That's right. Think about your vector:

(-3.18m)i + (4.73m)j

and then think about the vector in the opposite direction:

(3.18m)i + (-4.73m)j

Use inverse tangent on both of them:

on yours: arctan( 4.73 / -3.18 ) = arctan( -1.48742)
on the other: arctan ( -4.73 / 3.18 ) = arctan(-1.48742)

and that's the problem. Most calculators can't tell the difference between the two cases, so the answer it gives is either the true answer that you're looking for, or it's in the opposite direction from what you want (180 degrees away).

So in your case, you would need to recognize that your vector is in the second quadrant, but the calculator is giving you an angle in the fourth quadrant, so you need to add 180 degrees to the calculator answer to get the real answer.
 
  • #5
Ok awesome! Thanks for all your help!
 

1. What is an angle vector problem?

An angle vector problem is a mathematical problem that involves finding the magnitude and direction of a vector in terms of its components. It is commonly used in physics and engineering to solve problems involving forces, velocities, and displacements.

2. How do you solve an angle vector problem?

To solve an angle vector problem, you can use trigonometric functions such as sine, cosine, and tangent to find the magnitude and direction of the vector. You can also use vector addition and subtraction to solve more complex problems.

3. What are the components of a vector?

A vector has two main components: magnitude and direction. The magnitude is the length of the vector, and the direction is the angle at which the vector is pointing. These components can be represented by numbers or variables.

4. Can angle vector problems be solved graphically?

Yes, angle vector problems can be solved graphically using vector diagrams. By drawing the vectors and their components on a coordinate system, you can determine the magnitude and direction of the resulting vector visually.

5. What are some real-world applications of angle vector problems?

Angle vector problems are used in many fields, including physics, engineering, and navigation. For example, they can be used to calculate the velocity and acceleration of an object, determine the forces acting on a structure, or plot the course of a plane or ship.

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