MATH 21A Midterm: MATH 21A Harvard 21a Fall 17Practice9
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Tth 11:30 sebastian vasey: start by printing your name in the above box and check your section in the box to the left, do not detach pages from this exam packet or unstaple the packet, please write neatly. Answers which are illeg- ible for the grader cannot be given credit: show your work. Mark for each of the 20 questions the correct letter. There are unit vectors ~v and ~w in space for which |~v ~w| = 2. The vector h4, 5, 0i is perpendicular to the plane 5x + 4y + z = 2. The distance between the cylinders x2 + z2 = 1 and x2 + (z 3)2 = 1 is 3. The vector projection of h2, 3, 1i onto h1, 1, 1i is parallel to h1, 1, 1i. The equation sin( ) sin( ) = 2 in spherical coordinates de nes a plane.
