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.
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