MAT 228 Midterm: F08mt1sol
31 Jan 2019
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October 2, 2008: (12 pts) do the following. (a) carefully sketch 2v + w and v w: The dot product of two vectors is positive if the angle between them is acute, and negative if the angle between them is obtuse. The reason is that the dot product is de ned as where is the angle between the vectors. v w = kvkkwk cos , In our case here, we see from the diagram that is acute, so cos is positive, and thus the dot product will be positive. (c) carefully sketch projv w (the projection of w onto v). The projection is shown in bold: v w: (16 pts) given three points a = (1, 0, 1), b = (2, 1, 1), and c = (1, 0, 1), answer the following. (a) find ~ac and ~bc. ~ac = h1, 0, 1i h1, 0, 1i = h0, 0, 2i .
