Quiz 1 for MATH 105 SECTION 205
January 14, 2015
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1. Let u = h3, −4i and v = h1, 2i, then
(a) (1 point) Compute u + 2v.
(a)
(b) (1 point) Find the angle between u and v?
(b)
2. Let P be the plane which passes through the point (3, 0, 1) and is parallel to the plane 3x − 2y − z = 0, then
(a) (1 point) Write down the equation of the plane P .
(a)
(b) (1 point) Find the value of a such that the point (a, 2, 0) is on the plane P .
(b)
(c) (1 point) Find the value of b such that the plane P is orthogonal to the plane 2x − by = 1.
(c)
3. Let f (x, y) = ex and g(x, y) = y sin(xy), then
(a) (1 point) Compute fx (x, y).
(a)
(b) (1 point) Compute fy (x, y).
(b)
(c) (1 point) Compute gy (x, y).
(c)
4. (2 points) Sketch two level curves of the surface z =
x2
y2
+ .
9
16
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