The vector m {2; -1}, vector n {3; 2}. What is the angle (acute, right or obtuse) between these vectors?

Let’s find the modules of the given vectors:

| m | = √ ((2) ^ 2 + (-1)) ^ 2) = √5;

| n | = √ ((3) ^ 2 + 2 ^ 2) = √13.

Let’s calculate their dot product:

(m * n) = 2 * 3 + (-1) * 2 = 6 – 2 = 4.

By the definition of the scalar product, the equality is true:

(m * n) = | m | * | n | * cos (a), where a is the angle between vectors.

Then:

cos (a) = (m * n) / | m | * | n |;

cos (a) = 4 / √5 * √13 = √16 / 65.

Since 0 <cos (a) <1. Angle a – is acute.

Answer: the angle between the given vectors is acute.