Need help w/ arranging resultant vector with 3 other vectors. D:

In summary: In this case, you'll get a parallelogram. If you add vector C onto the vector combination of A and 2B, you'll get vector R. You can use the parallelogram method to find the magnitude and direction of vector R. Remember to draw the vectors to scale using the grid lines provided.
  • #1
Bensky
82
0

Homework Statement


Find the vector combination R = A + 2B - C. Grid lines are separated by 1 cm. When you submit your answer the third vector that you drew may disappear, but if you are correct you will have a green check mark near the grid. (Mac OS X use Netscape, Windows use IE.) A scratch vector is provided for your use if needed.

http://xs220.xs.to/xs220/07430/vectorhelp2.PNG

Homework Equations


none


The Attempt at a Solution


A x=-3 y=2
B x=-1 y=-1
C x=-2 y=1
R x=-3 y=-1

I tried using the tip to tail method for joining the vectors, but it didn't work since the vectors don't fit. Maybe I have to use the parallelogram method here? I really have no idea. :( Any help is appriciated.
 
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  • #2
You already know the equation for the resultant, and the components of each vector. If I have an equation for the resultant, say R = 2A - B, where A and B are vectors, and I know that A = < 1, 2 >, and B = < 3, 4 >, I can find the resultant by plugging the vector components into the resultant equation:

R = 2< 1, 2 > - < 3, 4 > = < 2, 4 > - <3, 4 >

Add the components:

< 2, 4 > - <3, 4 > = < -1, 0 >

Now we know that the resultant should be the vector < -1, 0 >, where -1 is the x component, and 0 is the y component.
 
  • #3
hotcommodity said:
You already know the equation for the resultant, and the components of each vector. If I have an equation for the resultant, say R = 2A - B, where A and B are vectors, and I know that A = < 1, 2 >, and B = < 3, 4 >, I can find the resultant by plugging the vector components into the resultant equation:

R = 2< 1, 2 > - < 3, 4 > = < 2, 4 > - <3, 4 >

Add the components:

< 2, 4 > - <3, 4 > = < -1, 0 >

Now we know that the resultant should be the vector < -1, 0 >, where -1 is the x component, and 0 is the y component.

Thanks, but I already have found the components of the vectors. I was asking how to do the graphical part, like where you arrange the vectors and the resultant. >_>
 
  • #4
Look at your equation, there's a minus signal in front of vector C. That equals to the sum of vector C, just in a opposite direction.
 

What is a resultant vector?

A resultant vector is a single vector that represents the combined effect of two or more other vectors. It is the sum of the individual vectors and takes into account both magnitude and direction.

How do I calculate the resultant vector?

To calculate the resultant vector, you will need to use vector addition. This involves breaking down the given vectors into their components (magnitude and direction) and then adding them together using vector addition rules. The resulting vector will be the resultant vector.

What are the steps to arranging a resultant vector with 3 other vectors?

The steps to arranging a resultant vector with 3 other vectors are as follows:

  1. Identify the given vectors and their components.
  2. Use vector addition to find the resultant vector.
  3. Draw a diagram to visualize the vectors and their directions.
  4. Arrange the vectors in a head-to-tail fashion, with the head of one vector connecting to the tail of the previous vector.
  5. The resulting vector from the head of the first vector to the tail of the last vector is the resultant vector.

What if the vectors are not in the same plane?

If the vectors are not in the same plane, you will need to use vector addition in three dimensions. This involves breaking down the vectors into their components in the x, y, and z directions, and then adding them together using vector addition rules. The resulting vector will be the resultant vector in three dimensions.

What are some real-world applications of arranging resultant vectors?

Arranging resultant vectors is a common technique used in physics and engineering to solve problems involving forces, velocities, and motion. It is also used in navigation and mapping, as well as in computer graphics and animation to simulate movement and motion.

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