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User Guide    

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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 vector addition
    →  `lambda (vec p + vec q) = lambda vec p + lambda vec q`

Distributive over Vector Addition

plain and simple summary

nub

plain and simple summary

nub

dummy

 •  A scalar multiplied by sum of two vectors equals sum of vectors multiplied by the scalar.

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 scalar is distributive over vector addition, is explained.


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

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

  • scalar
  • `lambda vec p + lambda vec q`
  • `lambda vec p + vec q`

The answer is '`lambda vec p + lambda vec q`'. This is 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 Vector Addition: Given scalar `lambda` and vectors `vec p, vec q`,
`lambda(vec p + vec q) = lambda vec p + lambda vec q`



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Given that `vec p = 6 vec q` and `vec r = 4 vec s`, which of the following equals `3 ( 2vec q+ 4/3 vec s)`?

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

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

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Considering that a vector has components as real numbers. Given that vector p = a i+b j+c k, vector q = e i + f j + g k and lambda where a,b,c,d,e,f,lambda are in real numbers, ;; What will be the result of lambda multiplied vector p + vector q?
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The answer is "lambda multiplied by vec p + lambda multiplied by vec q ". This is proven by multiplying the components individually by the scalar and using vector addition properties.
A scalar multiplied by sum of two vectors equals sum of vectors multiplied by the scalar.
Distributive over Vector Addition: Given scalar lambda and vectors p, vector q, lambda multiplied (vector p + vector q) = lambda times vector p + lambda times vector q
Given that vector p = 6 times vector q and vector r = 4 times vector s, which of the following equals 3 times, 2 vector q + 4 by 3 vector s?
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The answer is "vector p plus vector r".

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