# Solving Vector Cross Product Homework

• oreosama
In summary, the vectors a and b define a plane surface. The vector a x b is perpendicular to that surface, while the vectors a and b themselves are parallel to the surface. To find a possible vector parallel to the surface, we can use the fact that the cross product of two parallel vectors is the zero vector. Therefore, we can solve a linear system using the components of a and b to find a vector c that is parallel to the surface.
oreosama

## Homework Statement

vector a = (4i+3j-2k)
vector b = (2i-3j+2k)

1. a x b
2. 3a x 2b
3. |3a x 2b|

## The Attempt at a Solution

1. -12j - 18k

2. 6(a x b)
6(-12j - 18k)
-48j -108k

3. |6(a x b)|
sqrt(48^2 + 108^2)

sqrt(13968)

idk if I am using identities wrong or if I am way off, thanks for confirmation on right/wrong and any help

oreosama said:

## Homework Statement

vector a = (4i+3j-2k)
vector b = (2i-3j+2k)

1. a x b
2. 3a x 2b
3. |3a x 2b|

## The Attempt at a Solution

1. -12j - 18k

2. 6(a x b)
6(-12j - 18k)
-48j -108k

3. |6(a x b)|
sqrt(48^2 + 108^2)

sqrt(13968)idk if I am using identities wrong or if I am way off, thanks for confirmation on right/wrong and any help

Hi oreosama, welcome to PF. Your work is correct except a siliy mistake, How much is 12*6?

ehild

thanks for that.

using the same vectors

a=(4i+3j-2k)
b=(2i-3j+2k)

the vectors a and b define a plane surface. determine a possible vector perp. to that surface. determine a possible vector parallel to that surface.

perp: a x b= -12j -18k

assuming that's right..

parralel: I have no idea :(

i know parallel vectors just have scaler multiplier but I am working with 2 vectors(of which I am assuming intersect to create a plane?). I am pretty confused at this point so I am going to sleep and hope someone provides insight by the time i wake up. thanks for any help

If <a> and <b> are contained within the plane, then a vector parallel to <a> or <b> will also be parallel to the plane.
If two vectors are parallel, then their cross product is the zero vector. Therefore compute:
$$\vec{a}\, ×\,\vec{c} = 0$$ where $\vec{c}$ is the vector you want. You can solve a linear system of 3 variables, and get a dependence on the components of <c>.
Note: <b> can be used in place of <a>

The vectors a and b lay in the surface, and so do their linear combinations. All are parallel with the plane. (you can shift a vector parallel with itself, it is the same vector.)

ehild

## What is a vector cross product?

A vector cross product is a mathematical operation that takes two vectors as input and produces a third vector that is perpendicular to both of the input vectors. It is often used in physics and engineering to calculate the torque and angular momentum of a system.

## How do I solve vector cross product problems?

To solve a vector cross product problem, you need to follow a specific formula. First, take the cross product of the first component of the two vectors, then take the cross product of the second component of the two vectors, and finally take the cross product of the third component of the two vectors. Then, combine these three cross products to get the resulting vector.

## What are the applications of vector cross product?

The vector cross product has various applications in physics and engineering, such as calculating the torque and angular momentum of a system, determining the direction of a magnetic field, and calculating the force on a wire in a magnetic field. It is also used in computer graphics to create 3D images.

## What is the difference between vector cross product and dot product?

The vector cross product and dot product are two different mathematical operations involving vectors. The cross product produces a vector that is perpendicular to both input vectors, while the dot product produces a scalar value. Additionally, the cross product is only defined for three-dimensional vectors, while the dot product can be calculated for any number of dimensions.

## Can vector cross product be calculated for non-perpendicular vectors?

No, the vector cross product can only be calculated for perpendicular vectors. If the input vectors are not perpendicular, the resulting cross product will be zero. This is because the cross product measures the amount of perpendicularity between two vectors. If they are already perpendicular, the resulting cross product will be zero.

• Introductory Physics Homework Help
Replies
9
Views
1K
• Introductory Physics Homework Help
Replies
6
Views
797
• Introductory Physics Homework Help
Replies
4
Views
16K
• Introductory Physics Homework Help
Replies
1
Views
1K
• Introductory Physics Homework Help
Replies
1
Views
3K
• Engineering and Comp Sci Homework Help
Replies
2
Views
902
• Introductory Physics Homework Help
Replies
24
Views
1K
• Introductory Physics Homework Help
Replies
2
Views
3K
• Introductory Physics Homework Help
Replies
17
Views
864
• Introductory Physics Homework Help
Replies
6
Views
3K