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Understanding Properties of Cross Product

» **Vector cross Product is a vector with numerical expressions of real numbers **

→ properties of vector cross product is understood from the properties of real-numbers applied to the numerical expression

*plain and simple summary*

nub

*plain and simple summary*

nub

dummy

Cross product is a vector with numerical expression as components.

Properties of cross product are understood from properties of real numbers applied to the numerical expression representing the cross product.

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trek

*simple steps to build the foundation*

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In this page, you will learn about the fundamentals of understanding properties of vector cross product.

Starting on learning, "Understanding Properties of Cross Product". ;; In this page, you will learn about the fundamentals of understanding properties of vector cross product.

Given the following

`vec p = p_x i+p_yj+p_zk `

`vec q = q_x i+q_yj+q_zk `

`vec p xx vec q`

`quad quad = |(i, j, k),(p_x, p_y, p_z),(q_x, q_y, q_z)|`

Where `p_x, p_y, p_z, q_x, q_y, q_z in RR `

What is the result `vec p xx vec q`?

- a scalar
- a vector

The answer is 'a vector'

`vec p xx vec q = |(i, j, k),(p_x, p_y, p_z),(q_x, q_y, q_z)| `

`p_x, p_y, p_z, q_x, q_y, q_z in RR `

What are the x, y, z components of the result?

- numerical expressions of real numbers
- not numerical expressions as the terms are not numbers

The answer is 'numerical expressions of real numbers'

`vec p xx vec q = |p||q|sin theta hat n`

What is `|p||q|sin theta`?

- a numerical expression of real numbers
- not a numerical expression as the terms are not numbers

The answer is 'a numerical expression of real numbers'

To understand properties of cross product, the following are to be learned

• Closure Law

• Commutative Law

• Associative Law

• Distributive Law

• Modulus in cross product

In learning these, which of the following would help?

- Memorize each of the laws
- use the properties of real numbers to understand the cross product as numerical expression

The answer is 'use the properties of real numbers to understand the cross product as numerical expression'.

*comprehensive information for quick review*

Jogger

*comprehensive information for quick review*

Jogger

dummy

**Cross Product as Numerical Expressions: ** `vec p xx vec q = |(i, j, k),(p_x, p_y, p_z),(q_x, q_y, q_z)| `

where `p_x, p_y, p_z, q_x, q_y, q_z in RR `

`vec p xx vec q = |p||q|sin theta `

where `|p|, |q|, sin theta in RR `

The cross product is a numerical expression of real numbers.

**Properties of Cross Product: ** `vec p xx vec q = |(i, j, k),(p_x, p_y, p_z),(q_x, q_y, q_z)| ` is considered as numerical expressions and properties of real numbers are applied to understand properties of cross product.

*practice questions to master the knowledge*

Exercise

*practice questions to master the knowledge*

Exercise

To understand properties of cross product, which of the following number system is used?

- Integers
- Rational numbers
- Real Numbers
- None of the above

The answer is 'Real Numbers'

*your progress details*

Progress

*About you*

Progress

Given the following vector p = p x i + p y j + p z k;; vector q = q x i + q y j + q z k;; vector p cross vector q = determinant ;; What is the result of vector p cross vector q?

scalar

a scalar

vector

a vector

The answer is 'a vector'

What are the x, y, z components of the result of vector cross product?

1

2

The answer is 'numerical expressions of real numbers'

vector p cross vector q = magnitude p multiplied magnitude q sine theta, n hat;; What is magnitude p, magnitude q, sine theta?

1

2

The answer is 'a numerical expression of real numbers'

Cross product is a vector with numerical expression as components.

Cross Product as Numerical Expressions: vector p cross vector q = determinant; where p x, p y, p z, q x, q y, q z are real numbers. ;; vector p cross vector q = magnitude p multiplied magnitude q sine theta. Where magnitude p, magnitude q, sine theta are real numbers. The cross product is a numerical expression of real numbers.

To understand properties of cross product, the following are to be learned ;; closure law ;; commutative law;; associative law ;; distributive law;; modulus in cross product. In learning these, which of the following would help?

1

2

The answer is 'use the properties of real numbers to understand the cross product as numerical expression'.

Properties of cross product are understood from properties of real numbers applied to the numerical expression representing the cross product.

Properties of Cross Product: The cross product is considered as numerical expressions and properties of real numbers are applied to understand properties of cross product.

To understand properties of cross product, which of the following number system is used?

integers

Integers

rational

Rational numbers

real

Real Numbers

none;above

None of the above

The answer is "Real numbers"