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summary of this topic

Properties of Vector Multiplication by Scalar

Properties of Vector Multiplication by Scalar

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 »  multiplication of a vector by a scalar is distributive over scalar addition
    →  `(lambda + mu) vec p = lambda vec p + mu vec p`

Distributive over Scalar Addition

plain and simple summary

nub

plain and simple summary

nub

dummy

 •  A vector multiplied by sum of two scalars equals sum of the vector multiplied by the scalars.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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In this page, The property, Multiplication of vector is distributive over scalar addition, is explained.


Keep tapping on the content to continue learning.
Starting on learning the property "Distributive over Scalar Addition". ;; In this page, The property, Multiplication of vector is distributive over scalar addition, is explained.

What does 'distribute' mean?distributive property illustration

  • to trouble or disturb
  • to give to many

The answer is 'to give to many'.

Considering that a vector has components as real numbers, Given that `vec p = ai+bj+ck` and `lambda + mu` where `a,b,c,lambda,mu in bbb R`, What will be the result of `(lambda + mu) vec p`?Distributive property of vector multiplication by scalar

  • scalar
  • `lambda vec p + mu vec p`
  • `lambda + mu vec p`

The answer is '`lambda vec p + mu vec p`'. This can be proven by multiplying the components individually by the scalar and using vector addition properties.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Distributive Over scalar addition: Given scalars `lambda,mu` and vector `vec p`,
`(lambda+mu)vec p = lambda vec p + mu vec p`



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Given that `vec p = 3 vec q` and `vec r = 2 vec q`, which of the following equals `7 vec q`?

  • `vec p + vec r`
  • `vec p + 2 vec r`
  • `vec p - vec r`
  • `vec r - vec p`

The answer is '`vec p + 2 vec r`'

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What does 'distribute' mean?
trouble;disturb
to trouble or disturb
give;many
to give to many
The answer is 'to give to many'.
Considering that a vector has components as real numbers. Given that vector p = a i+b j+c k and lambda + mu; where a,b,c,lambda,mu are in real numbers. What will be the result of lambda + mu multiplied vector p?
1
2
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The answer is "lambda multiplied vector p plus mu multiplied vector p". This can be proven by multiplying the components individually by the scalar and using vector addition properties.
A vector multiplied by sum of two scalars equals sum of the vector multiplied by the scalars.
Distributive Over scalar addition: Given scalars lambda,mu and vector p ;; lambda plus mu multiplied vector p ;=; lambda multiplied vector p plus mu multiplied vector p
Given that vector p = 3 times vector q and vector r = 2 times vector q, which of the following equals 7 times vector q?
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The answer is "vector p + 2 times vector r"

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