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In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.continue

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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

*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*

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

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'