Vectors
Vector is a quantity specified by magnitude plus direction in space
Properties of vectors
Any vector is uniquely specified by its three components x, y, z which are projections of the vector on coordinate axes with unit vectors (such that )

The notation of vector with coordinates has the form
is 
Magnitude of vector (or its length) is defined by Pythagorean Theorem
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Adding vectors
Adding of vectors and is sum vector
The sum vector is determined by Parallelogram Rule of addition

Magnitude of sum vector is defined by Law of Cosines

where:
and are magnitudes of the vectors and 
is angle between them
Components of sum vector:
x = x1+ x2
y = y1+ y2
z = z1+ z2
The parallelogram rule of addition is partial case of general Polygon Rule used for adding several vectors 

Subtracting vectors
Subtracting of vectors and is vector difference
The vector difference is determined by Triangle Method of subtraction

Magnitude of vector difference

Components of vector difference:
x = x1 - x2
y = y1 - y2
z = z1 - z2
Scalar Product
Scalar (or dot) product of vectors and is scalar quantity defined by
where is angle between vectors and 
Properties of scalar product:
1) 
2) If then 
3) If then 
4) 
Vector product
Vector (or cross) product of vectors and is vector

The vector is normal to plane in which the vectors and lie (plane x-y) directed in accordance with Right-Hand Rule: when right palm is half-bent from to its thumb shows the direction of vector 
Magnitude of vector 

where is angle between vectors and 
Components of vector product:



Properties of vector product:
1) 
2) If then 
3) If then magnitude of vector product is 
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