Operations on scalars are the same as in elementary mathematics and algebra whereas operations on vectors obey the Triangle Law and Parallelogram Law of Addition.
Multiplication of a vector by a scalar:
The dimensions of λP is the product of the dimensions of λ and P.
Addition of vectors:
In the graphical method of vector addition either the Triangle Law of Addition or the Parallelogram Law of Addition is used.
Vectors obey the commutative and associative laws of addition. Addition of two vectors with equal magnitude but opposite direction results in a vector with zero magnitude called a null vector or a zero vector. In case of a null vector, you cannot specify direction.
To subtract two vectors the concept of addition of two vectors is used after reversing the direction of the second vector.