Quiz 2 KEY

# Quiz 2 KEY - y = 0 or both 2 Let P =(1 − 3 and Q =(3 2...

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Name: PID: TA: Sec. No: Sec. Time: Math 10C Quiz 2 Feb 8, 2008 1. Let f ( x,y ) = xy . Draw a contour diagram with contours at c = 1, c = 0, and c = 1. Describe in words what shape these contours are (ie, circles, ellipses, hyperbolas, lines, or some other shape). Solution: The contours at c = 1 and c = 1 are the hyperbolas y = 1 x and y = 1 x , respectively. The contour at c = 0 is the union of the x -axis and the y -axis (ie, all the points ( x,y ) satisfying either x = 0 or y = 0, or both).
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Unformatted text preview: y = 0, or both). 2. Let P = (1 , − 3) and Q = (3 , 2), and let v be the vector −→ PQ . a. Find a unit vector in the direction of v . Solution: v = 2 i + 5 j , so b v b = √ 29, and the unit vector u = 1 b v b v is given by 2 √ 29 i + 5 √ 29 j . b. Find a vector of length 4 pointing in the same direction as v . Solution: This vector is just 4 u = 4 √ 29 i + 20 √ 29 j ....
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