# Vector Arithmetics

Arithmetic operations of vectors are performed member-by-member, i.e., memberwise.

For example, suppose we have two vectors a and b.

> a = c(1, 3, 5, 7)
> b = c(1, 2, 4, 8)

Then, if we multiply a by 5, we would get a vector with each of its members multiplied by 5.

> 5 * a
[1]  5 15 25 35

And if we add a and b together, the sum would be a vector whose members are the sum of the corresponding members from a and b.

> a + b
[1]  2  5  9 15

Similarly for subtraction, multiplication and division, we get new vectors via memberwise operations.

> a - b
[1]  0  1  1 -

> a * b
[1]  1  6 20 56

> a / b
[1] 1.000 1.500 1.250 0.875

#### Recycling Rule

If two vectors are of unequal length, the shorter one will be recycled in order to match the longer vector. For example, the following vectors u and v have different lengths, and their sum is computed by recycling values of the shorter vector u.

> u = c(10, 20, 30)
> v = c(1, 2, 3, 4, 5, 6, 7, 8, 9)
> u + v
[1] 11 22 33 14 25 36 17 28 39