Notice

We and selected partners use cookies or similar technologies as specified in the cookie policy.
You can consent to the use of such technologies by closing this notice, by scrolling this page, by interacting with any link or button outside of this notice or by continuing to browse otherwise.
To find out more about the categories of personal information collected and the purposes for which such information will be used, please refer to our privacy policy.

California Consumer Notice

 0 AC +/- รท 7 8 9 ร 4 5 6 - 1 2 3 + 0 00 , =

# Vector Collinearity Check Calculator

## This calculator checks if two vectors are collinear (parallel) and gives a detailed solution.

Collinearity of vectors is the ratio of parallelism of vectors, so two nonzero vectors are collinear (parallel) if they lie on parallel lines or on one straight line.

Dimension of space
Specify the form of the first vector
Specify the form of the second vector

Enter the coordinates of the first vector
a̅ = { ; }

Enter the coordinates of the second vector
b̅ = { ; }

How to Check if Two Vectors Are Collinear (Parallel)

Example #1
Determine whether two vectors located in two-dimensional space are collinear (parallel). The coordinates of both vectors are given by points.
Coordinates of point A of vector AB: (5 ; 9)
Coordinates of point B of vector AB: (-2 ; 11)
Coordinates of point C of vector CD: (0 ; 12)
Coordinates of point D of vector CD: (-3 ; 1)

Step by step solution:

Calculate the coordinates of the first vector from two points A and B:

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

Calculate the coordinates of the second vector from two points C and D:

CD = {xD - xC  ; yD - yC} = {-3 - 0 ; 1 - 12} = {-3 ; -11}

Let us check if the vectors AB and CD have a coefficient of proportionality q (which has the same value for all equations in the system), for this we compose the system of equations and check whether the equality holds
ABx = q โ CDx
ABy = q โ CDy

 -7 = q โ (-3) then, q = - 7 -3
 = 7 3

 2 = q โ (-11) then, q = 2 -11
 = - 2 11

 7 3
 โ  - 2 11

 In the first equation, the coefficient of proportionality is 7 3
 , in the second - 2 11

 Therefore, the system is incompatible and has no solutions. The coordinates of vectors AB and CD are not proportional, which means that vectors AB and CD are not collinear.

Example #2
Determine whether two vectors located in two-dimensional space are collinear (parallel).
Vector coordinates a: (2 ; 6)
Vector coordinates b: (7 ; 21)

Step by step solution:

Let us check if the vectors a and b have a coefficient of proportionality q (which has the same value for all equations in the system), for this we compose the system of equations and check whether the equality holds
ax = q โ bx
ay = q โ by

 2 = q โ 7 then, q = 2 7

 6 = q โ 21 then, q = 6 21
 = 2 7

 2 7
 = 2 7

 In the first equation, the coefficient of proportionality is 2 7
 , in the second 2 7
 The coefficient of proportionality in each equation has the same value, therefore the coordinates of the vectors a and b are proportional and therefore the vectors are collinear. The value of the coefficient of proportionality is greater than zero, which means that vectors a and b are co-directed.

Example #3
Determine whether two vectors in three-dimensional space are collinear (parallel). The coordinates of both vectors are given by points.
Coordinates of point A of vector AB: (7; 0.2 ; 69)
Coordinates of point B of vector AB: (-1 ; 0 ; 2/8)
Coordinates of point C of vector CD: (-4 ; -6 ; 2)
Coordinates of point D of vector CD: (3 ; 0 ; 9)

Step by step solution:

Calculate the coordinates of the first vector from two points A and B:

AB = {xB - xA  ; yB - yA; zB - zA} = {-1 - 7 ; 0 - 0.2 ; 2/8 - 69} = {-8 ; 1/5 ; -275/4}

Calculate the coordinates of the second vector from two points C and D:

CD = {xD - xC  ; yD - yC; zD - zC} = {3 - (-4) ; 0 - (-6) ; 9 - 2} = {7 ; 6 ; 7}

Let us check if the vectors AB and CD have a coefficient of proportionality q (which has the same value for all equations in the system), for this we compose the system of equations and check whether the equality holds
ABx = q โ CDx
ABy = q โ CDy
ABz = q โ CDz

 -8 = q โ 7 then, q = - 8 7

 1/5 = q โ 6 then, q = 1/5 6
 = 1 30

 -275/4 = q โ 7 then, q = - 275/4 7
 = - 275 28

 - 8 7
 โ 1 30
 โ  - 275 28

 In the first equation, the coefficient of proportionality is - 8 7
 , in the second 1 30
 and in the third - 275 28

 Therefore, the system is incompatible and has no solutions. The coordinates of vectors AB and CD are not proportional, which means that vectors AB and CD are not collinear.

Example #4
Determine whether two vectors of vectors located in three-dimensional space are collinear (parallel).
Vector coordinates a: (0 ; 1 ; 7)
Vector coordinates b: (2 ; 0 ; 6)

Step by step solution:

Let us check if the vectors a and b have a coefficient of proportionality q (which has the same value for all equations in the system), for this we compose the system of equations and check whether the equality holds
ax = q โ bx
ay = q โ by
az = q โ bz

 0 = q โ 2 then, q = 0 2
 = 0

 1 = q โ 0

 7 = q โ 0

 Let's check, substitute the value of the coefficient in the equations

 0 =
 0
 โ 2

 1 โ
 0
 โ 0

 7 โ
 0
 โ 0
 Therefore, the system is incompatible and has no solutions. The coordinates of vectors a and b are not proportional, which means that vectors a and b are not collinear.
 You may also find the following calculators helpful Linear Algebra and Analytical Geometers Calculators Matrix Addition and Subtraction Calculator Matrix Multiplication Calculator Matrix Transpose Calculator Matrix Determinant Calculator Inverse Matrix Calculator Length of a Line Segment. Distance Between Points Online Calculator. Vector Coordinates Calculator From Two Points Vector Modulus (Length) Calculator Vector Addition and Subtraction Calculator Vector Dot Product Calculator. By Using the Length of the Vectors and Cosine of the Angle Between Vectors. Vector Dot Product Calculator. By Using Vector Coordinates. Vector Product Calculator. By Using Vector Coordinates. Vector Triple Product Calculator Vector Multiplication by Number Calculator Angle Between Vectors Calculator Vector Collinearity Check Calculator Vector Coplanarity Calculator Combinatorics Calculators Permutations of N Elements Calculator Combinations of N Elements by M Calculator Permutations of N Elements by M Calculator Numeral Systems Calculators Roman Numeral Calculator Roman Numerals From 1 to 3999 Numeral Systems Calculator Binary Calculator. Addition, Subtraction, Multiplication and Division of Binary Numbers. Fraction Calculators Simplifying Fractions Calculator Improper to Mixed Fraction Calculator Mixed Fraction to Improper Calculator Fractions Calculator With Step by Step Solution Raising a Fraction to a Power. Online Calculator. Decimal to Fraction Calculator Fraction to Decimal Calculator Compare Fractions Calculator Common Denominator Calculator Trigonometers Calculators Sine Calculator Cosine Calculator Tangent Calculator Cotangent Calculator Secant Calculator Cosecant Calculator Arcsine Calculator Arccosine Calculator Arctangent Calculator Arccotangent Calculator Arcsecant Calculator Arccosecant Calculator Calculators (Number theory) Mathematical Expressions Calculator Calculator Parentheses Prime Factorization Calculator Gcd and Lcm Calculator With Steps Gcd and Lcm calculator using Euclidean algorithm Gcd and Lcm Calculator for Any Number of Numbers Break Down the Number Into Its Place Value Divide a Number by a Ratio. Online Calculator With Steps Percentage Calculator With Steps Scientific Notation to Decimal Conversion Calculator Scientific Notation Converter Factorial Calculator With Steps Logarithm Calculator Quadratic Equations Calculator With Steps Remainder Calculator Root Calculator Decimal Period Calculator Big Number Calculator Rounding Numbers Calculator Properties of Roots and Exponents Calculator Complex Number Calculator Area Calculators Area of a Square Calculator Area of a Rectangle Calculator Math Trainers Addition Math Trainer Subtraction Math Trainer Multiplication Math Trainer Division Math Trainer Multiplication Table Math Trainer Online Preschool Counting Trainer Online Preschool Mindfulness Trainer Online Addition Subtraction Multiplication Division Math Trainer. Find the Correct Answer. Online Numeric Expression Trainer Converters Length Converter Speed Converter Acceleration Converter Physics Calculators Mechanics Speed Time Distance Calculator Acceleration Speed Distance Calculator Displacement Time Calculator Time Calculator Newton's Second Law Calculator Gravitational Force Calculator Momentum Calculator Impulse Calculator Object Weight Calculator Optics Light Reflection and Refraction Calculator Electricity and Magnetism Ohm's Law Calculator Coulomb's Law Calculator Electric Field Strength Calculator Point Electric Charge Calculator Q Force Acting on Charge Calculator Distance From Charge Calculator Potential Charge Energy Calculator Electric Field Potential Calculator Conductor and Sphere Capacitance Calculator Capacitors Capacitance of Parallel Plate, Cylindrical and Spherical Capacitors Calculator Electric Field Strength in Parallel Plate, Cylindrical and Spherical Capacitors Calculator Voltage (Potential Difference) of Parallel Plate, Cylindrical and Spherical Capacitors Calculator Distance Between Plates in Parallel Plate Capacitor Calculator Plate Area in Parallel Plate Capacitor Calculator Energy Stored in Charged Capacitor Calculator Energy Stored in Parallel Plate, Cylindrical and Spherical Charged Capacitors Calculator Volumetric Energy Density of Parallel Plate, Cylindrical and Spherical Capacitors Calculator Astronomy Calculators Object Weight on Other Planets Gravitational Acceleration on the Planets of the Solar System and Their Satellites Generators Random Number Generator Password Generator