3. Consider the ellipsoid x2 + 4y2 + z? = 18. Find the acute angle that the tangent plane at the point (1, 2, 1) makes with the xy – plane. Solution: To find the acute angle 0 between the tangent plane and the xy – plane, we have n1 = n = (2,16, 2) and n2 = (0,0, 1). This yields %3D In1 n2| ||n1||n2|| (2,16,2)-(0,0,1)| || (2,16,2)||||(0,0,1)|| cosê = cosê = (2v66)(1) V66 -1 COS 0 = 83° 66.

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