Find the angle between vectors a and b, if vector a = (1; 0), vector b = (2; 2)

Let’s find the modules of vectors:

| a | = √ (1 ^ 2 + 0 ^ 2) = 1;

| b | = √ (2 ^ 2 + 2 ^ 2) = √8.

Let’s calculate their dot product, which is determined by the sum of the product of their coordinates:

(ab) = 1 * 2 + 0 * 2 = 2.

The cosine of the angle between vectors is equal to the ratio of the dot product of vectors and their modules:

cos (a) = 2/1 * √8 = 1 / √2.

Then the angle itself is equal to:

a = arccos (1 / √2) = π / 4.

Answer: the value of the required angle is π / 4 or 45 degrees.