What Are the Basics of Calculating Cross Products in Vector Algebra?

[jst81161]

I was wondering if anyone could give me information the base of cross product all the problems I have been reading about so far have been in real depth I need to understand the basics first the problems given here are the beginning, if anyone can give me any help please do so, and thank you in advance

Homework Statement

calculate for

x cross product Y =


x cross product z =


y cross product (-z)=


a cross product b = where a= -ez and b= Bza cross product b= a= x + Y and b= Y

Homework Equations

a cross product b= -b cross product a

The Attempt at a Solution

Homework Statement

Homework Equations

The Attempt at a Solution

Homework Statement

Homework Equations

The Attempt at a Solution

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Homework Statement

Homework Equations

The Attempt at a Solution

 

[berkeman]

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[m2003]

The dot product and cross product are mathematical operations used in vector algebra. The dot product is used to find the scalar (numerical) value of the projection of one vector onto another, while the cross product is used to find the vector that is perpendicular to both of the original vectors.

To understand the basics of the cross product, it is important to first understand the concept of vectors. Vectors are quantities that have both magnitude (size) and direction. They are often represented by arrows, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction.

The cross product of two vectors, denoted by a x b, is a vector that is perpendicular to both a and b. This means that the cross product of two vectors will always be a vector that is perpendicular to both of the original vectors. This is often visualized as a vector that points out of the page or screen.

To calculate the cross product, we use the following formula:

a x b = (a2b3 - a3b2)i + (a3b1 - a1b3)j + (a1b2 - a2b1)k

Where a1, a2, and a3 are the components of vector a, and b1, b2, and b3 are the components of vector b.

Now, let's look at the given problems:

1. x cross product Y =
To calculate this, we need to find the components of x and Y. Since they are not given, we cannot provide a numerical answer. However, we can use the formula above to calculate the cross product.

2. x cross product z =
Similarly, we need to find the components of x and z to calculate this cross product.

3. y cross product (-z) =
Once again, we need to find the components of y and -z to calculate this cross product.

4. a cross product b = where a = -ez and b = Bz
Since the components of a and b are given, we can use the formula to calculate the cross product.

5. a cross product b = where a = x + Y and b = Y
Similarly, we can use the formula to calculate the cross product of these two vectors.

Remember, the cross product is a vector and the dot product is a scalar. They are two different operations used in vector algebra and have different properties and applications. It is important to understand