# Review 1 - MAC 2313 SUMMER 2010 Test 1 Review 1) State...

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MAC 2313 SUMMER 2010 Test 1 Review 1) State whether the following statements are True or False. If true give a brief justiﬁcation and if false give a counter example. Assume u and v to be arbitrary vectors in R 3 and k to be a scalar. a) | u × v | = | v × u | . b) u × ( v + w ) = u × v + u × w . c) v × ( u × w ) = ( v × u ) × w . d) ( u + v ) × v = u × v . e) k ( u × v ) = ( ku ) × v. f) If u · v = 0, then either u = 0 or v = 0. g) If w · ( u × v ) = 5, then v · ( w × u ) = 5. h) Two lines parallel to a plane are parallel. j) Two planes parallel to a line are parallel. 2) Find the distance from ( - 6 , 3 , 5) to the plane x - 2 y - 4 z = 8. 3) Find the point of intersection of the lines r = h 1 , 1 , 0 i + t h 1 , - 1 , 2 i and r = h 2 , 0 , 2 i + s h- 1 , 1 , 0 i . 4) Find the area of the triangle with vertices P (1 , 4 , 6), Q ( - 2 , 5 , - 1) and R (1 , - 1 , 1). 5) Find the equation of the line through the point (1 , 0 , 6) and perpendicular to the plane x +3 y + z = 5. 6) Find the equation of the plane that contains the line

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## This note was uploaded on 12/15/2011 for the course MAC 2313 taught by Professor Keeran during the Spring '08 term at University of Florida.

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Review 1 - MAC 2313 SUMMER 2010 Test 1 Review 1) State...

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