Vectors: solving for magnitude

In summary, the problem involves adding two vectors, A and B, with B having a magnitude of 9.0 m. The resulting sum is a third vector with a magnitude 6 times that of A, directed along the y-axis. To solve for the magnitude of A, the vectors must be broken down into x and y-components and added together. A possible solution method is to use the equation a + b = c and drawing a visual representation.
  • #1
FriskeCrisp
6
0
Vector A, which is directed along an x axis, is to be added to vector B, which has a magnitude of 9.0 m. The sum is a third vector that is directed along the y axis, with a magnitude that is 6 times that of A. What is the magnitude of A? (Enter your answer to 4 significant figures.)

So I know that vector B is 9 m. With the given information, I made the assumption that vector A is Vector A + 9. And finally, the third vector, the sum, would be 6(vector A). Am I on the right train of thought with the problem? To solve for the missing variables, can I use a + b = c?
 
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  • #2
Vectors have both magnitude and direction. You can't just add the magnitudes and ignore the directions. You will have to break up the vectors into x and y-components and add them. I suggest possibly drawing a picture.
 

1. What is a vector and how is it different from a scalar?

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

2. How do you solve for the magnitude of a vector?

To solve for the magnitude of a vector, you can use the Pythagorean theorem. The magnitude is equal to the square root of the sum of the squares of the vector's components. For example, if a vector has components x and y, the magnitude is equal to the square root of x^2 + y^2.

3. What is the importance of vectors in physics and engineering?

Vectors are important in physics and engineering because they allow us to represent quantities that have both magnitude and direction. This is essential for understanding and solving problems related to motion, forces, and other physical phenomena.

4. Can vectors be added or subtracted?

Yes, vectors can be added or subtracted as long as they have the same number of dimensions. This is done by adding or subtracting the corresponding components of the vectors. The result is a new vector with a magnitude and direction that combines the original vectors.

5. How can vectors be represented visually?

Vectors can be represented visually as arrows, with the length of the arrow representing the magnitude and the direction of the arrow indicating the direction of the vector. This is known as a vector diagram and is a useful tool for understanding and solving vector problems.

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