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...Practice problems answers to some vector geometry given two vectors a and b do the equations v kak determine uniquely if so nd an explicit formula of in terms answer is yes clearly are not orthogonal then there no solution assume let angle between kbk kakkvk sin cos hence kvk that length determines s also arccos therefore perpendicular such x depending weather oriented or more elegant we may otherwise form basis one can write as linear combination xa yb za y z real numbers wewill take inner products with first xkak but ykbk implies finally zka bk think determinant expressing cross product ka tangent planes lines find points on surface where plane parallel ax by cz d c i their corresponding normal n ai bj ck j k our level set f m tm q exists rsuchthat other words need solve system xy e unit graph at point r corre sponding show graphs g share o has check have same see this consider well dened really since...