How do you find the direction of a vector given its magnitude and angle?

In summary, the problem involves finding the magnitudes of Vector A and Vector B, given that Vector A points in the negative x direction, Vector B points at an angle of 33.0 degrees above the positive x axis, Vector C has a magnitude of 13 m and points in a direction 37.0 degrees below the positive x axis, and the sum of Vector A, Vector B, and Vector C is equal to zero. To solve the problem, a vector diagram is constructed and the three vectors are written in terms of their coordinates. The horizontal and vertical components of the vectors are then set equal to zero and solved for the unknowns a and b, which can be used to find the magnitudes of Vector A and Vector
  • #1
egadda2
7
0

Homework Statement



Vector A points in the negative x direction. Vector B points at an angle of 33.0 degrees above the positive x axis. Vector C has a magnitude of 13 m and points in a direction 37.0 degrees below the positive x axis.

Given that , Vector A + Vector B + Vector C = 0, find the magnitudes of Vector A and Vector B.

Homework Equations





The Attempt at a Solution

 
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  • #2
Construct a vector diagram. You should get a closed triangular loop from the three vectors.
 
  • #3
egadda2 said:

Homework Statement



Vector A points in the negative x direction. Vector B points at an angle of 33.0 degrees above the positive x axis. Vector C has a magnitude of 13 m and points in a direction 37.0 degrees below the positive x axis.

Given that , Vector A + Vector B + Vector C = 0, find the magnitudes of Vector A and Vector B.

Homework Equations





The Attempt at a Solution

Let a = the magnitude of A = |A|
Let b = |B|
Let c = |C| = 13 (given)

Write the three vectors in terms of their coordinates, like this:
A = -a*i + 0*j
B = b*cos(33 deg)*i + b*sin(33 deg)*j
C = 13*cos (-37 deg)*i + 13*sin(-37 deg)*j

For the three vectors to sum to zero, their horizontal components have to add to zero, and their vertical components have to add to zero. Set up these two equations and solve for the unknowns a and b. Once you have these values you can find the magnitudes of A and B.
 

1. What is a vector?

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

2. How is the magnitude of a vector calculated?

The magnitude of a vector is calculated using the Pythagorean theorem, which states that the magnitude (M) of a vector with components a and b is equal to the square root of the sum of the squares of the components (M = √(a² + b²)).

3. How is the direction of a vector represented?

The direction of a vector is represented using either the angle it makes with a reference axis (such as the x-axis) or by its direction in relation to the four cardinal directions (north, east, south, west).

4. How do you find the direction of a vector given its magnitude and angle?

To find the direction of a vector given its magnitude and angle, you can use trigonometric functions such as sine, cosine, and tangent. The angle is typically measured counterclockwise from the positive x-axis.

5. Can a vector have a negative magnitude or direction?

No, a vector cannot have a negative magnitude or direction. The magnitude of a vector is always a positive number, and the direction is usually represented as a positive angle or a positive direction in relation to the reference axis. However, a vector can have negative components, which means it is pointing in the opposite direction.

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