Question about vector angular separation

Find two unit vectors each of which makes equal angles with the vectors u = 4i + j +k, v = i + j, and w = 2i + j + k.

Answer 1

[Roger Stafford]

This sounds like homework, so I will only give hints. The cosine of the angle between two vectors is equal to their dot product divided by the product of the magnitude (norms) of the two vectors. Utilizing this appropriately will give you two equations for the unknown vectors' components, and making them unit vectors gives you the third equation. You will find that these three equations have two solutions and these will be your desired vectors.

Answer 2

[Andrei Bobrov]

U1 = [4 1 1; 1 1 0;2 1 1]; %your vectors
U1norm = sqrt(sum(U1.^2,2));
U1e = bsxfun(@rdivide,U1,U1norm);
v = bsxfun(@minus,U1e(1:2,:),U1e(3,:));
v2 = cross(v(1,:),v(2,:));

out1 = v2/norm(v2);
angle1 = acosd(U1*out1'./U1norm);
out2 = -out1;
angle2 = acosd(U1*out2'./U1norm);