MATH 251 Midterm: MATH 251 TAMU 251-Spring 11 Exam 1s11 Solutions
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Let l be the line given by parametric equations x = 3 + 2t, y = 2 + 5t, and z = 1 4t. What is the equation of the plane that contains the point (3, 1, 5) and is perpendicular to. Solution: a the vector n = h2, 5, 4i is parallel to l, and so will make a normal vector to the plane. Since we want (3, 1, 5) to be on the plane, we see that (a) is the correct answer. Let f (x, y) = 2 cos(xy2 3y). Solution: d we rst calculate fx = 2 sin(xy2 3y) y2, and then nd that fxy = 4y sin(xy2 3y) 2 cos(xy2 3y) (2xy 3)y2, which simpli es to (d). Consider the curve in 3-space de ned by the vector function r(t) = h3 sin(t), 4 cos(t), 4ti.
