Finding dot product, cross, and angle between 2 vectors

In summary: If you have a specific question about a particular step that's confusing you, I'll try to help. I think the "positive z component" just means that the vector points upwards, but I'm not sure.In summary, the given vectors A and B lie in the yz and xz planes, respectively, at certain angles from the +y and +x axes. They both have positive z components and specific magnitudes. The task is to find the dot product, cross product, and angle between the two vectors. To do this, they can be represented in unit vector notation and the dot and cross products can be calculated using their components. The "positive z component" indicates the direction of the vector along the z-axis
  • #1
PAstudent
47
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Homework Statement


[/B]
Vector A lies in the yz plane 63.0 degrees from the +y axis, has a positive z component, and has a magnitude 3.20 units. Vector B lies in the xz 48.0 degrees from the +x axis, has positive z component, and has magnitude 1.40 units.

a) find A dot B
b) find A x B
c) the angle between A and B

Homework Equations


dot product and cross product [/B]

The Attempt at a Solution



What I am trying is to put them in unit vector notation like:
A= axi+ayj so A= [3.20cos(63.0)]i+[3.20sin(63.0)] and then the same for vector B

Then once I have those components I could easily do dot and cross product. My question is what does that "has a positive z component " have to do with anything? And is my setup correct?[/B]
 
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  • #2
PAstudent said:

Homework Statement


[/B]
Vector A lies in the yz plane 63.0 degrees from the +y axis, has a positive z component, and has a magnitude 3.20 units. Vector B lies in the xz 48.0 degrees from the +x axis, has positive z component, and has magnitude 1.40 units.

a) find A dot B
b) find A x B
c) the angle between A and B

Homework Equations


dot product and cross product [/B]

The Attempt at a Solution



What I am trying is to put them in unit vector notation like:
A= axi+ayj so A= [3.20cos(63.0)]i+[3.20sin(63.0)] and then the same for vector B

Then once I have those components I could easily do dot and cross product. My question is what does that "has a positive z component " have to do with anything? And is my setup correct?[/B]
For example, vector B could make an angle of 48° above or below the +x-axis. The "positive z-component" tells you which side of the +x-axis to draw this vector.

I find in these cases making a simple sketch usually clarifies things a bit.
 
  • #3
So would there be a z hat in the calculations of the dot and cross or does it just tell you the location of the vector? Because I am still trying to figure out how to find the i and j to be able to find the products
 
  • #4
PAstudent said:
So would there be a z hat in the calculations of the dot and cross or does it just tell you the location of the vector? Because I am still trying to figure out how to find the i and j to be able to find the products
It seems you have three-dimensional vectors here, but I haven't sketched them out or anything. You'll have to work thru the verbal descriptions, and make some sketches as I suggested.
 

1. What is the dot product of two vectors?

The dot product of two vectors is a mathematical operation that results in a scalar value. It is calculated by multiplying the corresponding components of the two vectors and then adding them together. The dot product is also known as the inner product or scalar product.

2. How do you calculate the cross product of two vectors?

The cross product of two vectors is a mathematical operation that results in a vector. It is calculated by taking the cross product of the two vectors and using the right-hand rule to determine the direction of the resulting vector. The magnitude of the resulting vector is equal to the product of the magnitudes of the two vectors multiplied by the sine of the angle between them.

3. What is the significance of the angle between two vectors?

The angle between two vectors is important because it can provide information about the relationship between the two vectors. For example, if the angle between two vectors is 90 degrees, it means that the two vectors are orthogonal or perpendicular to each other. On the other hand, if the angle is 0 degrees, it means that the two vectors are parallel.

4. Can the dot product and cross product be used for any type of vectors?

The dot product and cross product can only be used for vectors in three-dimensional space. They cannot be used for vectors in higher dimensions, such as four-dimensional space. Additionally, the dot product and cross product are only defined for vectors with real-valued components.

5. What are some real-world applications of finding the dot product, cross product, and angle between two vectors?

The dot product, cross product, and angle between two vectors have many real-world applications. They are used in physics, engineering, and computer graphics to calculate forces, moments, and angles. They are also used in navigation and robotics for determining positions and orientations. In addition, they are used in machine learning and data analysis for feature extraction and dimensionality reduction.

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