Solution: Linear Constraints in a Plane

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Given the plane x(α,β) = α+ β+ c, sketch lines for α = 1, 2, 3 and then for β = 1, 2, 3. 

In this case, we've chosen c = (2,1,0) drawn in greena = (2,0,0) drawn in blue, and b = (1,1,0) drawn in red. In general, vectors a and b determine the plane to which c reaches from the coordinate origin. When α is constant and β varies, we are constrained to a red line in the plane, parallel to vector b. When β is constant and α varies, we are constrained to a blue line in the plane, parallel to vector a. We can try different values of α and β using the sliders. We can then watch how x changes by following its vector and by reading the updating text box.

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© David Hestenes 2005, 2014