HW_02_S

HW_02_S - Ph1a Solutions 2 Che-Fung Chan...

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Unformatted text preview: Ph1a Solutions 2 Che-Fung Chan (cchan@caltech.edu), Fall 2004 Each homework problem is worth 5 points. Please disregard the point values listed on the problem itself. Use these instead. 2.1 Serway 7.9(6th)/7.13(5th) (5 points) Basic concept (2 points) The angle between two vectors vector A and vector B is given by = arccos vector A vector B vextenddouble vextenddouble vextenddouble vector A vextenddouble vextenddouble vextenddouble vextenddouble vextenddouble vextenddouble vector B vextenddouble vextenddouble vextenddouble 2.1.a (1 point) vector A = [3 , 2 , 0], vector B = [4 , 4 , 0] vector A vector B = 3 4 + ( 2) ( 4) + 0 = 20 vextenddouble vextenddouble vextenddouble vector A vextenddouble vextenddouble vextenddouble = radicalbig 3 2 + ( 2) 2 = 13 3 . 61 vextenddouble vextenddouble vextenddouble vector B vextenddouble vextenddouble vextenddouble = radicalbig 4 2 + ( 4) 2 = 4 2 5 . 66 = arccos parenleftbigg vector A vector B bardbl vector A bardblbardbl vector B bardbl parenrightbigg arccos(0 . 981) . 197 rad or 11 . 3 2.1.b (1 point) vector A = [ 2 , 4 , 0], vector B = [3 , 4 , 2] vector A vector B = 22, vextenddouble vextenddouble vextenddouble vector A vextenddouble vextenddouble vextenddouble = 2 5 4 . 47, vextenddouble vextenddouble vextenddouble vector B vextenddouble vextenddouble vextenddouble = 29 5 . 39 arccos( . 914) 2 . 72 rad or 156 2.1.c (1 point) vector A = [1 , 2 , 2], vector B = [0 , 3 , 4] vector A vector B = 2, vextenddouble vextenddouble vextenddouble vector A vextenddouble vextenddouble vextenddouble = 3, vextenddouble vextenddouble vextenddouble vector B vextenddouble vextenddouble vextenddouble = 5 arccos 0 . 133 1 . 44 rad or 82 . 3 2.2 Serway 11.6(6th)/11.14(5th) (5 points) The answer is no. This is because the cross product always yields a vector perpendicular to both of the input vectors. Formally, this can be expressed by the identity vector A parenleftBig...
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This note was uploaded on 03/30/2010 for the course PH 1a taught by Professor Goodstein during the Fall '07 term at Caltech.

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HW_02_S - Ph1a Solutions 2 Che-Fung Chan...

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