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summary of this topic

Properties of Dot Product

Properties of Dot Product

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Understanding Properties of Dot Product


 »  Vector Dot Product is numerical expression of real-numbers

    →  individual components on `3` axes are real numbers

    →  the components multiply and add

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

Understanding Properties of Dot Product

plain and simple summary

nub

plain and simple summary

nub

dummy

Dot product is a numerical expression with terms as real numbers.

Properties of dot product is understood from properties of real numbers applied to the numerical expression representing the dot product.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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


Keep tapping on the content to continue learning.
Starting on learning - "Understanding Properties of Dot Product". ;; In this page, you will learn about the fundamentals of understanding properties of vector dot product.

Given the following
`vec p = p_x i+p_yj+p_zk `

`vec q = q_x i+q_yj+q_zk `

`vec p cdot vec q = p_xq_x+p_yq_y+p_zq_z `
Where `p_x, p_y, p_z, q_x, q_y, q_z in RR `
Can you guess what will be the result `vec p cdot vec q`?

  • a real number
  • an integer
  • a fraction
  • a whole number

The answer is 'a real number'

`vec p cdot vec q = p_xq_x+p_yq_y+p_zq_z `
`p_x, p_y, p_z, q_x, q_y, q_z in RR `

What is `p_xq_x+p_yq_y+p_zq_z`?

  • a numerical expression with terms as real numbers
  • not a numerical expression as the terms are not numbers

The answer is 'a numerical expression with terms as real numbers'

`vec p cdot vec q = |p||q|cos theta `

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

  • a numerical expression with terms as real numbers
  • not a numerical expression as the terms are not numbers

The answer is 'a numerical expression with terms as real numbers'

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

 •  Closure Law

 •  Commutative Law

 •  Associative Law

 •  Distributive Law

 •  Modulus in dot product

In learning these, which of the following would help?

  • Memorize each of the laws
  • use the properties of real numbers to understand the dot product as numerical expression

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

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Dot Product as Numerical Expression: `vec p cdot vec q = p_xq_x+p_yq_y+p_zq_z `
where `p_x, p_y, p_z, q_x, q_y, q_z in RR `
`vec p cdot vec q = |p||q|cos theta `
where `|p|, |q|, cos theta in RR `
The dot product is a numerical expression of real numbers.

Properties of Dot Product: `vec p cdot vec q = p_xq_x+p_yq_y+p_zq_z ` is considered as an numerical expression and properties of real numbers are applied to understand properties of dot product.



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

To understand properties of dot 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 dot vector q = p x q x + p y q y + p z q z ;; Where p x, p y , p z, q x, q y, q z are real numbers. Can you guess what will be the result vector p dot vector q ?
real
a real number
integer
an integer
fraction
a fraction
whole
a whole number
The answer is 'a real number'
vector p dot vector q = p x q x + p y q y + p z q z ;; Where p x, p y , p z, q x, q y, q z are real numbers. What is p x q x + p y q y + p z q z?
1
2
The answer is 'a numerical expression with terms as real numbers'
vector p dot vector q = magnitude of p multiplied magnitude of q multiplied cos theta. What is the result of the dot product?
1
2
The answer is 'a numerical expression with terms as real numbers'
Dot product is a numerical expression with terms as real numbers.
Dot Product as Numerical Expression: vector p dot vector q = p x q x + p y q y + p z q z ;; where p x, p y, p z, q x, q y, q z are real numbers. ;; Vector p dot vector q = magnitude p multiplied magnitude q multiplied cos theta ;; where magnitude p, magnitude q, cos theta are real numbers ;; the dot product is a numerical expression of real numbers.
To understand properties of dot product, the following are to be learned ;; closure law ;; commutative law;; associative law;; distributive law ;; modulus in dot product. ;; In learning these, which of the following would help?
memorize;each;laws
Memorize each of the laws
use;properties;real;numbers;understand
use the properties of real numbers to understand the dot product as numerical expression
The answer is 'use the properties of real numbers to understand the dot product as numerical expression'.
Properties of dot product is understood from properties of real numbers applied to the numerical expression representing the dot product.
Properties of Dot Product: vector p dot vector q = p x q x + p y q y + p z q z ;; is considered as an numerical expression and properties of real numbers are applied to understand properties of dot product.
To understand properties of dot product, which of the following number system is used?
integers;integer
Integers
rational
Rational numbers
real
Real Numbers
none;above
None of the above
The answer is 'Real Numbers'

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