Vector Cross Product and Magnitude Calculation

In summary, the conversation discusses finding the vector product of two 2D vectors and determining the magnitude of the resulting vector. The cross product can be evaluated using the formula U x V = |U||V| * sin(angle between U and V). The conversation also clarifies that this is not a 3D problem and provides the correct answer of -17.0k and 17.0.
  • #1
elpermic
29
0
2D or 3D vector problem??

Homework Statement


Find the vector product of Vector A cross Vector B(expressed in unit vectors) of the two vectors. What is the magnitude of the vector product?


Homework Equations


Vector A= 5.00i + 2.00j
Vector B= 3.00i - 1.00j



The Attempt at a Solution



I know how to get the dot product of the two, but how do I find the cross product??
 
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  • #2


This vector problem is 2D. You don't have a k component to represent the third dimension.

The cross product can be evaluated by

U x V = |U||V| * sin(angle between U and V)

|U| this means the "magnitude of U".

Hope that helps.

Thanks
Matt
 
  • #3


The answer says -17.0k and 17.0. So shouldn't this mean it's a 3D problem? My teacher never taught me this in class and gave us 2 vector problems like this.
 
  • #4


No this is not a 3D problem. Where could the third dimension come from? The answers are equal and opposite in magnitude, that doesn't mean there is a third dimension.

What is your attempt at the solution? Can you find the magnitudes of the Vector A and Vector B?

Thanks
Matt
 
  • #5


The magnitude of vector a is 5.38, vector b 3.16. I calculated the angle between the two to be 40.2 degrees. So I took ABsin(40.2) and got my answer is 11.0. The answer in the back says -17.0k, 17.0. I'm confused.. Is the book wrong or me?
 
  • #6


Nevermind, I solved it.
 
  • #7


Good then, hope I helped you out.

Thanks
Matt
 

Related to Vector Cross Product and Magnitude Calculation

1. What is a vector in 2D or 3D space?

A vector is a mathematical object that represents both magnitude and direction in 2-dimensional or 3-dimensional space. It is commonly represented by an arrow, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction.

2. What is the difference between a 2D and 3D vector?

The main difference between a 2D and 3D vector is the number of dimensions they exist in. A 2D vector exists in a two-dimensional plane, while a 3D vector exists in a three-dimensional space. This means that a 2D vector has two components, usually represented as (x,y), while a 3D vector has three components, usually represented as (x,y,z).

3. How do you add or subtract 2D or 3D vectors?

To add or subtract 2D or 3D vectors, you simply add or subtract the corresponding components of the vectors. For example, to add two 2D vectors (a,b) and (c,d), the resulting vector would be (a+c, b+d). Similarly, to subtract (a,b) from (c,d), the resulting vector would be (c-a, d-b).

4. What is the dot product of 2D or 3D vectors?

The dot product of two vectors is a scalar quantity that is calculated by multiplying the corresponding components of the vectors and then adding them together. In 2D space, the dot product can be calculated as (ax*bx + ay*by), where ax and ay are the components of vector A, and bx and by are the components of vector B.

5. How do you find the magnitude and direction of a 2D or 3D vector?

The magnitude of a vector is the length of the vector, which can be calculated using the Pythagorean theorem. In 2D space, the magnitude of a vector (x,y) is given by √(x² + y²). The direction of a vector can be found using trigonometric functions such as sine, cosine, and tangent. In 2D space, the direction of a vector (x,y) can be found using the arctangent function, given by tan⁻¹(y/x).

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