13 calculusof vector valued functions 13 1 vector valued functions lt section 14 1 preliminary questions 1 which one of the following does not parametrize a line a r t ...
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...Calculusof vector valued functions lt section preliminary questions which one of the following does not parametrize a line r t b ti tj tk c solution thisisaparametrizationofthelinepassingthroughthepoint inthedirectionparalleltothevector since using parameter s we get this is parametrization through origin with direction v in particular points at and are collinear what projection etk onto xz plane path curve traced by e k z ex cost sint circle theparametricequations x y theprojection cos sin xy therefore weexpressy terms parabola yz hence nd as function again center i j contained holds weconcludethat radius centered point may howdothepathsr around unit differ thetwopathsdescribetheunitcircle however ast increasesfromto thepointonthepathsinti costj movesinaclockwisedirection whereas on costi sintj moves counterclockwise three same space d allthe curves except for lie vertical identify each parametric equations...