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# Vector Multiplication by Number Calculator

## This calculator multiplies a vector by a number and gives a detailed solution to all stages of the calculation.

Dimension of space
Specify the form of the vector

Enter the coordinates of the vector
a̅ = { ; }

Enter the value of the number q by which you want to multiply the vector
q =

How to Multiply a Vector by a Number in 2d and 3d Space

Example #1
Let's multiply the vector in two-dimensional space by the number q. Vector coordinates are given by points.
Coordinates of point A of vector AB: (5 ; 9)
Coordinates of point B of vector AB: (-2 ; 11)
The numbers q by which you need to multiply the vector AB = 12

Step by step solution:

In order to multiply a vector by a number, it is necessary to multiply each coordinate of the vector by a given number.

Let's calculate the coordinates of the first vector at two points A and B:

AB = {xB - xA  ; yB - yA} = {-2 - 5 ; 11 - 9} = {-7 ; 2}

AB โ q = {ABx โ q ; ABy โ q} = {-7 โ 12 ; 2 โ 12} = {-84 ; 24}

Example #2
Let's multiply a vector in three-dimensional space by q.
Vector coordinates a: (5 ; 9 ; -2)
The number q by which you need to multiply the vector a = 2.6

Step by step solution:

In order to multiply a vector by a number, it is necessary to multiply each coordinate of the vector by a given number.
a โ q = {ax โ q ; ay โ q ; az โ q} = {5 โ 2.6 ; 9 โ 2.6 ; -2 โ 2.6} = {13 ; 117/5 ; -26/5} = {13 ; 23.4 ; -5.2}
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