Free problems arranged by topic
 Kinematics Dynamics Conservation laws Thermodynamics Waves Electricity Magnetism Optics Fluids and elasticity Ideal gas AC current

 Free problems: all problems
 Kinematics Dynamics Conservation laws Thermodynamics Waves Electricity Magnetism Optics Fluids and elasticity Ideal gas AC current

..

# Physics problems: vectors

Vectors are very important in Physics and especially in physics problems.

Why?

Because many physical quantities, such as velocity, acceleration, force, electric field, magnetic field, and others are vectors.

Vectors carry the information about magnitude and direction of physical quantity.

For example, we know the vector of velocity. It means that we know the direction of the motion and the magnitude of velocity (speed).

## Properties of vectors:

- two vectors are equal if they are equal in both magnitude and direction:

- multiplication by a number:

Vector (where is the positive number) has the same direction as vector , but its length is times larger then the length of vector .

Vector (where is the negative number) has the direction opposite to the direction of vector , but its length is times larger then the length of vector

- scalar (dot) product:

is a scalar (not vector) =

If the vectors are orthogonal then the scalar product is 0

- vector product:

is a VECTOR, the magnitude of which is

Vector is orthogonal to the plane formed by vectors and .

If two vectors have the same direction then vector product is 0

..
 home vectors units