What is the Angle Between Two Vectors with Equal Magnitudes and a Given Sum?

In summary, the conversation discusses how to determine the angle between two vectors, A and B, when their sum is a given vector, 12.1 j. The suggested method is to use the formula for the magnitude of the resultant vector, R, which involves the magnitudes of A and B and the cosine of the angle between them. Alternatively, the law of cosines can be used.
  • #1
Melchior25
30
0
Hey everyone,

So I'm completely stumped on this question and I have no clue on how to even start. Any help would be greatly appreciated.

Vectors A and B have equal magnitudes of 23.0. If the sum of A and B is the vector 12.1 j, determine the angle between A and B.

Thanks in advance.
 
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  • #2
Draw the resultant vector of magnitude 12.1N first, then draw the two vectors A and B that would give the resultant direction in the direction that you drew the 12.1N force in. Complete the parallelogram. Then use some trigonometry.
 
  • #3
In this case, to save a lot of time, I would suggest the OP just use the formula for the magnitude of the resultant R of two forces P and Q, given by:

R^2 = P^2 + Q^2 + 2PQcos(theta).

The magnitude of R is given.
 
  • #4
Yeah I could agree, just use the law of cosines.
 

What is a vector?

A vector is a mathematical quantity that has both magnitude (size) and direction. It is typically represented by an arrow pointing in the direction of the vector, with the length of the arrow representing the magnitude. Vectors are commonly used in physics, engineering, and mathematics.

How do you add vectors?

To add two vectors, you must first make sure they are in the same coordinate system. Then, you can add the corresponding components of each vector to get the resulting vector. For example, if you have vectors A = (3, 2) and B = (-1, 4), the resulting vector would be C = (2, 6).

What is the difference between a vector and a scalar?

A vector has both magnitude and direction, while a scalar only has magnitude. For example, velocity is a vector quantity because it has both speed (magnitude) and direction, while distance is a scalar quantity because it only has magnitude.

How do you find the magnitude of a vector?

The magnitude of a vector can be found using the Pythagorean theorem. If the vector is represented by (x,y), the magnitude is equal to the square root of the sum of the squares of the components, or √(x²+y²).

What are some common applications of vectors?

Vectors are used in a variety of fields, such as physics, engineering, and computer graphics. They are often used to represent forces, velocities, and positions in physical systems. Vectors are also used in computer graphics to represent the direction and intensity of light, and in video games for character movement and collision detection.

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