Vector Problems

Vector Problems - Mathematics 375 Some problems about...

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Mathematics 375 Some problems about vectors 1. If a quadrilateral OABC in R 2 is a parallelogram having A and C as op- posite vertices, prove that A + 1 2 ( C - A ) = 1 2 B . What geometric theorem about parallelograms follows from this equation? Show that every vector 2. Let A = ± 2 1 ² , B = ± 1 3 ² . Show that every vector C = ± c 1 c 2 ² can be written as αA + βB . Express α, β in terms of c 1 , c 2 . 3. Let A = ± 2 1 ² , B = ± 1 3 ² . (i) Draw the set of points C = αA + βB which is obtained as α, β run through all real numbers such that α + β = 1. (ii) Draw the set of points C = αA + βB which is obtained as α, β run through all real numbers such that 0 α 1, 0 β 1. 4. Let A = 1 - 2 3 , B = 3 1 2 . (i) Find a vectors of length 1 which are parallel to (i) A + B , (ii) A - 2 B . (ii) Find scalars α , β so that C = αA + βB is a nonzero vector with h C, B i = 0. 5.
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Vector Problems - Mathematics 375 Some problems about...

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