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Properties of Cross Product

Properties of Cross Product

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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

Understanding Properties of Cross Product

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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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.


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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'

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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"

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