# What is the difference between vectors and phasors?

I've seen both the terms vectors and phasors be used when it comes to AC circuits. I'm still kind of confused with how to clearly distinguish the two terms. I get that in a vague sense, the complex quantities used in AC circuits can be referred by using both terms. But I think phasors is more correct? From my understanding, phasors seem to be a subset of vectors. A phasor is a rotating vector and the direction is an angular distance from the reference in the rotation.

I just decided to ask here since I haven't seen any StackExchange question talk about these two words in depth.

• Ah, I agree with all your points. (1) As you said, vector is a general concept that can be used in many disciplines, such a physics, robotics, ... (2) Phasor is usually used in AC circuits. (3) A basic tutorial for newbies is this: Phasor Diagrams and Phasor Algebra - Electronics Tutorials: electronics-tutorials.ws/accircuits/phasors.html. Happy learning together, Cheers. – tlfong01 Jan 27 at 15:07

Phasors are complex numbers. They are scalars, although we can also define them in terms of magnitude and angle on the complex plane.

Vectors are vectors. Vectors have both magnitude and direction.

While either one can be defined by two real numbers, they are not the same.

As far as EE goes, the main difference between them is the multiplication operator that applies.

When you multiply two complex numbers (phasors, for example) you get a product with a magnitude equal to the product of the magnitudes of the multiplicand and the multiplier, and an angle that is equal to the sum of the angles of the multiplicand and the multiplier.

When you multiply two vectors, you must choose (depending on the problem you're trying to solve) either scalar multiplication (dot product) or vector multiplication (cross product).

If you choose (or require) the dot product, you get a product with magnitude equal to the projection of the multiplcand onto the multiplier, and with no angle at all---the product isn't even a vector, it's a scalar.

If you choose (or require) the cross product, you get a product with a magnitude equal to the product of the two operands' magnitudes times the sine of the angle between them. And with a direction perpendicular to both of the operands (thus, not even in the vector space defined by the two operands).

I'm still kind of confused with how to clearly distinguish the two terms.From my understanding, phasors seem to be a subset of vectors

1.phasors are not subset of vectors ! In a game of mathematics every thing is defined on the basis of its properties and there are many properties of phasors that vectors doesn't obey e.g differentiation or integration property and many properties of vectors that phasors don't obey e.g dot or cross product of vectors.

I think phasors is more correct?

1. Of course phasors is more correct because of its properties(specially integration and differentiation properties which is missing in vectors )