Vectors Calculator ·

06 May 2024, 00:00

Vectors Calculator Image to Crop

Enter vector A

Given the 2 vectors A and B you entered
calculate the angle θ between them:

Calculate pieces of the angle formula

cos(θ) =	A · B
	\|\|A\|\| * \|\|B\|\|

Determine the vector dot product A · B:

Rewrite our vectors in terms of coordinates:

(a1) = ()
(b1) = ()

Multiply the respective vector components:

A · B = a1b1
A · B = ·
A · B = 0
A · B = 0

Calculate the length (magnitude) of A

Rewrite the vector in terms of coordinates:

(a1) = ()

The formula for this is below:

||A|| = Square Root(a12)
||A|| = Square Root(2)
||A|| = √0
||A|| = √0
||A|| = 0

Calculate the length (magnitude) of B

Rewrite the vector in terms of coordinates:

(b1) = ()

The formula for this is below:

||B|| = Square Root(b12)
||B|| = Square Root(2)
||B|| = √0
||B|| = √0
||B|| = 0

Plugging in our values to the angle formula, we get:

cos(θ) =	0
	(0)(0)

cos(θ) =	0
	0

cos(θ) = NAN

θradians = NAN

Convert our angle to degrees from radians

Angle in Degrees =	Angle in Radians * 180
	π

θdegrees =	NAN * 180
	π

θdegrees =	NAN
	π

θdegrees = NAN°

You have 1 free calculations remaining

What is the Answer?

θdegrees = NAN°

How does the Vectors Calculator work?

Free Vectors Calculator - Given 2 vectors A and B, this calculates:
* Length (magnitude) of A = ||A||
* Length (magnitude) of B = ||B||
* Sum of A and B = A + B (addition)
* Difference of A and B = A - B (subtraction)
* Dot Product of vectors A and B = A x B
A ÷ B (division)
* Distance between A and B = AB
* Angle between A and B = θ
* Unit Vector U of A.
* Determines the relationship between A and B to see if they are orthogonal (perpendicular), same direction, or parallel (includes parallel planes).
* Cauchy-Schwarz Inequality
* The orthogonal projection of A on to B, projBA and and the vector component of A orthogonal to B → A - projBA
Also calculates the horizontal component and vertical component of a 2-D vector.
This calculator has 1 input.

What 1 formula is used for the Vectors Calculator?

||A|| = Square Root(a12 + a22 + a32)

For more math formulas, check out our Formula Dossier

What 14 concepts are covered in the Vectors Calculator?

anglethe figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. cauchy schwarz inequalitythe lengths of the dot product of vectors is less than or equal to the product of the lengths of the vectorscosinecos(θ) is the ratio of the opposite side to the hypotenuse.directionthe line or course on which something is goingdistanceinterval between two points in time
d = rtinequalitya relation which makes a non-equal comparison between two numbers or other mathematical expressions.
>, <, ≤, ≥lengththe measurement or extent of something from end to endmagnitudethe size, extent, or importance of something orthogonalTwo perpendicular lines - two lines forming a 90 degree angleorthogonalTwo perpendicular lines - two lines forming a 90 degree angleperpendiculartwo lines which intersect to form a right angleproductThe answer when two or more values are multiplied togetherprojectionthe transformation of points and lines in one plane onto another plane by connecting corresponding points on the two planes with parallel lines.vectordirected line segment