Question about cross and dot product

In summary, the conversation involves finding the dot product and cross product of two vectors, p1 and p2, and determining their perpendicularity and parallelism. The question also asks about the direction of a unit vector, r^. It is unclear what r is and how it relates to the problem. More information is needed to fully understand the problem.
  • #1
leonne
191
0

Homework Statement


There are two points p1 pointing up p2 pointing right

Homework Equations


The Attempt at a Solution


I need to find [tex]\stackrel{\rightarrow}{p1}[/tex] * r^

[tex]\stackrel{\rightarrow}{p2}[/tex] X p1^

[tex]\stackrel{\rightarrow}{p2}[/tex]* r^

they got [tex]\stackrel{->}{p1}[/tex] * r^ =0 why is that? i know if they are perpendicual than they =0 but not sure where r^ is pointing

[tex]\stackrel{->}{p2}[/tex] X p1^ =p2 well i know when 2 vectors are paralle the = 0 so i am guess when they are perpendicular they are p2 , but only one is a vector not sure if that matters.

[tex]\stackrel{->}{p2}[/tex]* r^ = p well i am guessing from this, that r^ is parallel with p2. that's why with p1 its 0, its perpendicular, but how do we find out which way r^ is pointing?

thxs
 
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  • #2
leonne said:

Homework Statement


There are two points p1 pointing up p2 pointing right
What do you mean that one "points up" and the other "points right"? A point doesn't have direction. Do you mean vectors?
leonne said:

Homework Equations





The Attempt at a Solution


I need to find [tex]\stackrel{\rightarrow}{p1}[/tex] * r^
What is r? Is r^ supposed to be a unit vector?
leonne said:
[tex]\stackrel{\rightarrow}{p2}[/tex] X p1^

[tex]\stackrel{\rightarrow}{p2}[/tex]* r^

they got [tex]\stackrel{->}{p1}[/tex] * r^ =0 why is that? i know if they are perpendicual than they =0 but not sure where r^ is pointing
If two vectors are perpendicular, their dot product is zero. The vectors themselves are not necessarily zero vectors.
leonne said:
[tex]\stackrel{->}{p2}[/tex] X p1^ =p2 well i know when 2 vectors are paralle the = 0 so i am guess when they are perpendicular they are p2 , but only one is a vector not sure if that matters.
If two vectors are parallel, then one is a scalar multiple of the other. Also, their cross product is the zero vector.
leonne said:
[tex]\stackrel{->}{p2}[/tex]* r^ = p well i am guessing from this, that r^ is parallel with p2. that's why with p1 its 0, its perpendicular, but how do we find out which way r^ is pointing?
Not much of what you wrote makes sense. Please include all of the given information for this problem.
 

1. What is the difference between the cross product and the dot product?

The cross product is a vector operation that results in a vector that is perpendicular to both of the original vectors. The dot product is a scalar operation that results in a single number, representing the magnitude of the projection of one vector onto the other.

2. When should I use the cross product versus the dot product?

The cross product is useful for determining the direction of a vector perpendicular to two other vectors, or for calculating the area of a parallelogram. The dot product is useful for calculating the angle between two vectors, or for determining the component of one vector in the direction of another.

3. How do I calculate the cross product and dot product?

The cross product can be calculated using the formula: a x b = |a||b|sin(theta) where a and b are the two vectors and theta is the angle between them. The dot product can be calculated using the formula: a · b = |a||b|cos(theta) where a and b are the two vectors and theta is the angle between them.

4. What are some real-world applications of the cross and dot product?

The cross product is commonly used in physics and engineering, such as in calculating torque and angular momentum. It is also used in computer graphics to determine the orientation of objects in 3D space. The dot product has applications in physics, such as in calculating work and energy, as well as in statistics and machine learning.

5. Is there a geometric interpretation of the cross and dot product?

Yes, the cross product can be interpreted as the area of a parallelogram formed by the two vectors, and the dot product can be interpreted as the projection of one vector onto the other. This can be visualized using vector diagrams and geometric representations.

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