A =

## Enter vector B

B =

Determine the vector operation A ÷ B:

## Rewrite our vectors in terms of coordinates:

(a1, a2, a3) = (12, 9, 6)
(b1, b2, b3) = (4, 3, 2)

## Divide the respective vector components:

A ÷ B = (a1 ÷ b1 , a2 ÷ b2 , a3 ÷ b3 )
A ÷ B = (12 ÷ 4, 9 ÷ 3, 6 ÷ 2)
A ÷ B = (3, 3, 3)

## Expresed in vector format, we have:

 3 3 3
Calculate the length (magnitude) of A / B

## Rewrite the vector in terms of coordinates:

(a / b1, a / b2, a / b3) = (3, 3, 3)

## The formula for this is below:

||A / B|| = Square Root(a / b12 + a / b22 + a / b32)
||A / B|| = Square Root(32 + 32 + 32)
||A / B|| = √9 + 9 + 9
||A / B|| = √27
||A / B|| = 5.1961524227066

##### 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?

angle
the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
cauchy schwarz inequality
the lengths of the dot product of vectors is less than or equal to the product of the lengths of the vectors
cosine
cos(θ) is the ratio of the opposite side to the hypotenuse.
direction
the line or course on which something is going
distance
interval between two points in time
d = rt
inequality
a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
>, <, ≤, ≥
length
the measurement or extent of something from end to end
magnitude
the size, extent, or importance of something
orthogonal
Two perpendicular lines - two lines forming a 90 degree angle
orthogonal
Two perpendicular lines - two lines forming a 90 degree angle
perpendicular
two lines which intersect to form a right angle
product
The answer when two or more values are multiplied together
projection
the transformation of points and lines in one plane onto another plane by connecting corresponding points on the two planes with parallel lines.
vector
directed line segment