Some Vector Math

public Vector3 vector;
Vector3 axis = Vector3.up;
float angle = 45.0f;

// Rotate a Vector3 by an angle on a given axis
vector = Quaternion.AngleAxis(angle, axis) * vector;

// Flatten a Vector3 on the Y-axis
float oldMagnitude = vector.magnitude;
vector = new Vector3(vector.x, 0, vector.z).normalized * oldMagnitude;