Question about vector angular separation
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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.
回答（2 个）
Roger Stafford
2014-9-12
2 个投票
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.
Andrei Bobrov
2014-9-18
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);
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2014-9-18
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