Vector Calculator 3D
Vector A
Vector B
Dot Product (A·B)
12
Cross Product (A×B)
(27, 6, -13)
|A| Magnitude
3.7417
|B| Magnitude
8.775
Angle between A and B
68.5624°
FAQ
Everything about vector math
What is the dot product?
The dot product A·B = ax·bx + ay·by + az·bz is a scalar measuring how much two vectors point in the same direction. If A·B = 0 the vectors are perpendicular.
What is the cross product?
The cross product A×B produces a vector perpendicular to the plane of A and B with magnitude |A||B|sin(θ). If A×B = 0 the vectors are parallel or antiparallel.
How do you compute the angle between two vectors?
Use cos(θ) = (A·B) / (|A|·|B|). Then θ = arccos of that value. If A·B > 0 acute, < 0 obtuse, = 0 right.
What is the difference between the dot and the cross product?
The dot product returns a number, and it says how much two vectors point the same way. The cross product returns a vector instead, one perpendicular to both of them.
How is the angle between two vectors worked out?
You divide the dot product by the product of the two magnitudes: the result is the cosine of the angle. A value close to zero means the vectors are nearly perpendicular.
What is the magnitude of a vector?
It is its length, the square root of the sum of the squares of the components. It is what you need to normalise a vector, that is, to reduce it to unit length while keeping its direction.