I constructed the technical figure embedded below. I wonder how to draw red arc to denote angle $\alpha$
between two blue vectors. (Actually, I add the desired output using Inkscape.)
The Asymptote code is pasted below.
import three;
import graph3;
size(200);
pen solid=linetype(new real[]);
pen longdashed=linetype(new real[] {10,8});
pen dashed=linetype(new real[] {3,8});
currentprojection=perspective(1/2,-1/4,1/4.4);
pen bg=gray(0.9)+opacity(0.1);
draw(surface((0,0,0.5)--(1,0,0.5)--(1,1,0.5)--(0,1,0.5)--cycle),bg);
draw((0,0,0)--(1,0,0), solid);
draw((0,0,0)--(0,1,0), longdashed);
draw((1,0,0)--(1,1,0), solid);
draw((0,1,0)--(1,1,0), longdashed);
draw((0,0,1)--(1,0,1), solid);
draw((0,0,1)--(0,1,1), solid);
draw((1,0,1)--(1,1,1), solid);
draw((0,1,1)--(1,1,1), solid);
draw((0,0,0)--(0,0,1), solid);
draw((1,0,0)--(1,0,1), solid);
draw((1,1,0)--(1,1,1), solid);
draw((0,1,0)--(0,1,1), longdashed);
draw((0.5,0,0.5)--(0.5,1,0.5));
draw((0,0.5,0.5)--(1,0.5,0.5));
draw((0,0,0)--(1,1,1),dashed);
draw((1,0,0)--(0,1,1),dashed);
// Blue vectors
draw((0.5,0.5,0.5)--(1,1,1),blue,Arrow3);
draw((0.5,0.5,0.5)--(1,0.5,0.5),blue, Arrow3);