114S11Final-m

# 114S11Final-m - 1. Let P be a point on the plane 3x + y 2z...

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1 . Let P be a point on the plane 3 x + y - 2 z = 2 and let Q be a point on the plane 3 x + y - 2 z = 5. Let v be the vector that points from P to Q . Which of the following cannot be true? (A) | v | = 10 (B) | v | = 100 (C) v · (3 i + j - 2 k ) = 0 (D) | v × (3 i + j - 2 k ) | = 0 (E) | v × (3 i + j - 2 k ) | = 100 (F) The x -coordinate of v is zero. (G) The y -coordinate of v is zero. (H) The z -coordinate of v is zero.

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2 . In October 2010, Josh Scobee of the Jacksonville Jaguars kicked a remarkable last- second 60-yard (180 feet) ﬁeld goal to beat the Indianapolis Colts. The football left the ground with an initial horizontal velocity of 45 feet per second toward the goalpost and an initial upward velocity of 67 feet per second. The crossbar of the goalpost is 10 feet high. By how many feet did the ball clear the crossbar? (Assume the acceleration due to gravity is 32 ft/sec 2 and ignore wind resistance.) (A) 2 feet (B) 4 feet (C) 6 feet (D) 8 feet (E) 10 feet (F) 12 feet (G) 14 feet (H) 16 feet
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## This note was uploaded on 04/04/2012 for the course MATH 114 taught by Professor Temkin during the Fall '07 term at UPenn.

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114S11Final-m - 1. Let P be a point on the plane 3x + y 2z...

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