Lambert's Cosine Law, Computing Diffuse Reflection

[DorumonSg]

Lambert's Cosine Law, Computing Diffuse Reflection :

I have 2 coordinates (5, 6, 0) the light source and (2.3, 1.92, 0) the plane. The diffuse coefficient is 0.6 and the light source intensity is 200.

So using the Lambert's Cosine Law,

I need to take 0.6 * 200 * the dot product of the normalized vectors of (5, 6, 0) and (2.3, 1.92, 0) right?

The model solution I have is 0.6 * 200 = 120.

I am wondering is that because both coordinates are on the same (XY) plane such that there is 0 degree difference between the 2 coordinates? So cos 0 is 1?

Is that the case?

If that's the case, does that mean :

Whenever I see any 2 coordinates on the same plan like (X1, 0, Z1), (X2, 0, Z2), I can just use cos 0?

And I only need to calcalate the cos theta if both coordinates are are on different planes?

And also I tried to compute the dot product of (5, 6, 0) and (2.3, 1.92, 0) after normalizing them of course, but I did not get 1?

 

[lippyka]

So what am I doing wrong here?The answer is correct, since the two coordinates are on the same plane (XY), the angle between them is 0°. Therefore, the dot product of the normalized vectors will be 1 and the final result of the diffuse reflection will be 120. When the two coordinates are on the same plane, the cosine of the angle between them is 1. In all other cases, you need to calculate the cosine of the angle between them. To calculate the dot product, you need to normalize both vectors first, then multiply them component-wise and take the sum of the products.