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12.1-2soln

# 12.1-2soln - MATH 231 Group Work Quiz Related 1 Determine...

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MATH 231 Group Work Quiz Related 1. Determine whether the points lie on a straight line: (a) (1 , 2 , 3), (4 , 5 , 6), and (7 , 8 , 9). (b) ( - 1 , - 5 , 1), (1 , 2 , 5), and (3 , 9 , 9). Answer: (a) Yes. (b) Yes. 2. Find the unit vector in the direction of the given vector: (a) h 2 , 0 , 0 i (b) 4 i + 2 j - 3 k (c) h 1 , 3 , 4 i (d) h 2 , - 3 , 7 i Answer: (a) h 1 , 0 , 0 i , (b) 1 29 h 4 , 2 , - 3 i (c) 1 26 h 1 , 3 , 4 i (d) 1 62 h 2 , - 3 , 7 i 3. Show that the equation represents a sphere. Compute the center and radius. 4 x 2 + 4 y 2 + 4 z 2 = 1 - 16 y + 8 x Answer: Dividing by 4, we find that x 2 + y 2 + z 2 = 1 4 - 4 y + 2 x . Thus, 1 4 = x 2 - 2 x + y 2 + 4 y + z 2 = ( x - 1) 2 + ( y + 2) 2 + z 2 - 5 . This gives us that ( x - 1) 2 + ( y + 2) 2 + z 2 = 21 4 , so the center is (1 , - 2 , 0) and the radius is 21 2 . 4. Name all equal vectors in the figure shown. A B C D E Answer: There are an awful lot of these. Just for a sample, here are some: ---→ AEB = --→ AB = ----→ ADEB 1

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---→ ABC = ---→ AEC = ----→ ADEC = ------→ ADEBC = ----→ AEBC --→ AD = ----→ ABCD = ------→ AEBCD = -------→ ADEBCD = ----→ AECD ---→ ECD = -----→ EBCD = ----------→ EBCDEBCD 5. A Los Angeles woman walks west at a speed of 4 mph. Suddenly, there is a violent earthquake and the ground beneath her begins to shift north at a speed of 7 mph. Find the speed and direction of the
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