Scaling vectors

When a vector is scaled, it only changes in magnitude, not direction. As with addition and subtraction, scaling is a component-wise operation. Unlike addition and subtraction, a vector is scaled by a scalar, not another vector.

Visually, a scaled vector points in the same direction as the original vector, but it has a different length. The following figure shows two vectors: (2, 1) and (2, 4). Both vectors share the same direction, but the magnitude of the second vector is longer:

Figure 2.4: Vector scaling

To implement vector scaling, multiply every component of the vector by the given scalar value.

Implement the scale function by overloading the * operator in vec3.cpp. Don't forget to add the function declaration to vec3.h:

vec3 operator*(const vec3 &v, float f) {

    return vec3(v.x * f, v.y * f, v.z * f);

}

Negating a vector can be done by scaling the vector by -1. When negating a vector, the vector maintains its magnitude but changes its direction.