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Unformatted text preview: HW-1 solution 1. For the two vectors zyxA2and zyxB32, find (a) BAand BA, (b) component of Balong A, (c) angle between Aand B, (d) BA, (e) BABA. Solution:(a) zyxzyxzyxBA23)32()2(74.3)2()1(3||222BA(b) 22.1)1(211)1(32)2(1||222AAB(c) 327.13)2()1(213||||cos222222BABA, =cos-1(0.327)=70.89o(d) zyx75132-1-21zyxBA(e) zyxBAABBABABBAABABA142102)()()()(.2. A,B, and Care three vectors pointing from the origin of a coordinate to three points A, B, and C, respectively. Find the distance between the origin to the ABC plane and the area of the ABC triangle. Express your result in terms of A,B, and Cvecotrs. Solution:The ABC plane can be defined by the two vectors CAand CB. Thus, the surface normal direction is along vector ACCBBABCCABACBCA)()(. The distance from the origin to the ABC plane is the projection of...
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- Fall '09