What is the Vector Sum of Two Vectors with Equal Magnitude and Different Angles?

In summary, the two vectors a and b have equal magnitude of 29 m and angles θ1 = 31° and θ2 = 105°. To find the x-component of their vector sum r, we use the equation x = 29cos31 + 29cos105. Similarly, the y-component sum is found using the equation y = 29sin31 + 29sin105. The magnitude of the vector sum can be found using the Pythagorean theorem, while the angle that their vector sum r makes with the positive direction of the x-axis can be found using trigonometric functions. It is important to note that the second vector points towards the y-axis while the first one points away.
  • #1
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Homework Statement


The two vectors a and b in the figure have equal magnitude of 29 m and the angles are θ1 = 31° and θ2 = 105°. Find the x-component of their vector sum r. Find y-component sum. Magnitude of the vector sum? Find the angle that their vector sum r makes with the positive direction of the x-axis.


Homework Equations





The Attempt at a Solution



Ok i am confused as to why this won't work.
x = 29cos31 + 29cos105
y = 29sin31 + 29sin105

The second vector/magnitude points towards the y-axis and the first one points away. i can not seem to insert a picture.
 
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  • #2
Looks good to me. Why do you think that's wrong? I'm assuming you're not making a simple mistake like confusing degrees and radians.
 
  • #3
i mean i think it is right. i put that answer into lon capa and it said it was wrong, so i figured i was doing something wrong.
 

What is a vector sum in x and y directions?

A vector sum in x and y directions is a mathematical operation that involves adding together two or more vectors in the x and y direction. This results in a new vector that represents the combined magnitude and direction of the original vectors.

How do you calculate a vector sum in x and y directions?

To calculate a vector sum in x and y directions, you must first determine the individual components (magnitude and direction) of each vector. Then, add the x components together and the y components together to get the final x and y values for the new vector. Finally, use the Pythagorean Theorem to calculate the magnitude of the new vector and use trigonometry to determine its direction.

What is the significance of the angle in a vector sum?

The angle in a vector sum represents the direction of the resulting vector. It is measured in degrees or radians and is determined using trigonometry. The angle is important because it tells us the direction in which the vector is pointing and provides additional information about the vector's magnitude and direction.

Can a vector sum have a negative magnitude?

Yes, a vector sum can have a negative magnitude. This occurs when the individual vectors being added have opposite directions and cancel each other out. In this case, the resulting vector will have a magnitude that is equal to the difference between the two individual vectors' magnitudes.

How is a vector sum in x and y directions represented graphically?

A vector sum in x and y directions can be represented graphically using a coordinate plane. The individual vectors are plotted as arrows with their tails at the origin, and the resulting vector is drawn from the tail of the first vector to the head of the last vector. The length and direction of the resulting vector can then be measured and determined using the coordinate plane.

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