How to Calculate Angle Between Two Vectors in C++

Vector mathematics is a branch of mathematics that deals with vectors, which are geometric objects with magnitude and direction. For example, the angle formed by a vector’s tails equals the angle formed by two vectors.

We should note that the angle formed by the two vectors remains between 0° and 180°. This article discusses how to calculate the angle between two vectors.

Calculate Angle Between Two Vectors in C++

We can calculate the angle of a vector, A, by taking the dot product of A and another vector, B. The dot product is calculated by multiplying their magnitudes and adding their angles. Let’s learn it below.

Dot Product in C++

The dot product is one of the mathematical operations that accept two vectors and returns a scalar. So, for example, we can calculate an angle of the vector, A, by taking the dot product of A and another vector, B.

The dot product is calculated by multiplying their magnitudes and adding their angles. The magnitude of the vector is the length of the line segment from its origin to its tip, while the direction of the vector refers to its specific orientation.

Steps to Find the Angle in 2D and 3D Plane

The steps to find the angle between two vectors in 2D and 3D planes are as follows:

• Declare two vectors with their lengths and direction.
• Find the magnitude of each vector.
• Calculate the dot product of these two vectors.
• Find the angle between the two vectors by using θ = Cos-1 [(a · b) / (|a| |b|)], if the vectors are in 2D plane.
• If the vectors are in a 3D plane, use this formula θ = Cos-1 [(a · b · c) / (|a| |b| |c|)]

Apart from the 2D and 3D planes, there is a critical exception you need to know as a programmer.

When your vectors are situated within a plane with a known normal vector n rather than randomly placed, the axis of rotation will then be oriented in the same direction as n, and the orientation of n will fix an orientation for that axis.

In this situation, you can modify the θ = Cos-1 [(a · b) / (|a| |b|)] by adding n to the determinant to increase its size.

Example

float Angles(const x &a, const y &b) {
  float d = dot(a, b) / (length(v0) * length(v1));
  return acos(demo(d, 3, 4f)) * RAD2DEG;
}