Common quaternion operations

Like vectors, quaternions also have component-wise operations. Common

component-wise operations are adding, subtracting, multiplying, or negating

quaternions. Component-wise quaternion multiplication multiplies a quaternion

by a single scalar value.

Since these functions are component-wise, they just perform the appropriate action on similar components of the input quaternions. Implement these functions in quat.cpp and add declarations for each function in quat.h:

quat operator+(const quat& a, const quat& b) {

    return quat(a.x+b.x, a.y+b.y, a.z+b.z, a.w+b.w);

}

quat operator-(const quat& a, const quat& b) {

    return quat(a.x-b.x, a.y-b.y, a.z-b.z, a.w-b.w);

}

quat operator*(const quat& a, float b) {

    return quat(a.x * b, a.y * b, a.z * b, a.w * b);

}

quat operator-(const quat& q) {

    return quat(-q.x, -q.y, -q.z, -q.w);

}

These component-wise operations don't have much practical use by themselves. They are the building blocks for building the rest of the quaternion functionality on. Next, you're going to learn about the different ways to compare quaternions.