Finding the Direction of Resultant Vector: A Vector Addition Problem

In summary, the question is asking to find the resultant of the given vectors and determine its direction counterclockwise from the positive x-axis. To do this, one must first find the magnitude of the resultant vector by using trig to find the x and y components of each vector and summing them. The angle of the resultant vector can then be determined by taking the tangent of Ry/Rx. A graphical sketch can also be helpful in determining the angle.
  • #1
sycho2
4
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The question is find the resultant of the vectors shown in the figure below. (Take a = 20.8°, b = 54.0° and c = 29.7°.)

I got the resultant vector to be 1.9units, it also tells me to find the direction counterclockwise from the positive x-axis. I'm not sure how to do that, is it asking me the degrees? I'm just confused what the question is asking for.
 
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  • #2
sycho2 said:
The question is find the resultant of the vectors shown in the figure below. (Take a = 20.8°, b = 54.0° and c = 29.7°.)

I got the resultant vector to be 1.9units, it also tells me to find the direction counterclockwise from the positive x-axis. I'm not sure how to do that, is it asking me the degrees? I'm just confused what the question is asking for.
Yes, once you find the magnitude of the resultant vector, usually by using trig to find the x and y components of each vector, summing those components into the Rx and Ry components of the resultant, then the angle of the resultant vector is the angle whose tangent is Ry/Rx. Be sure to draw a rough graphical sketch, and properly detrmine its angle as measured ccw from the positive x axis.
 
  • #3
Um, what "figure below"?
 

1. What is a vector and how is its direction determined?

A vector is a quantity that has both magnitude (size) and direction. Its direction is determined by its starting point and ending point, and can be represented by an arrow. The direction of a vector is usually measured in degrees or radians from a reference point, such as the positive x-axis.

2. How do you find the direction of a vector using its components?

To find the direction of a vector using its components, you can use trigonometric functions. First, find the inverse tangent of the ratio of the y-component to the x-component. This will give you the angle in radians. Then, convert the angle to degrees by multiplying by 180/π.

3. Can the direction of a vector change?

Yes, the direction of a vector can change. Vectors can be moved or rotated, which changes their direction. However, the magnitude of a vector remains constant.

4. How is the direction of a vector represented mathematically?

The direction of a vector can be represented mathematically using unit vectors. A unit vector is a vector with a magnitude of 1 that points in a specific direction. By multiplying a unit vector by a scalar value, you can change the magnitude and direction of the vector.

5. Why is it important to know the direction of a vector?

The direction of a vector is important because it helps us understand the movement or change of a physical quantity in a specific direction. In fields such as physics and engineering, knowing the direction of a vector is crucial in solving problems and making accurate predictions about the behavior of objects or systems.

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