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7.5: Scalar and Vector Projections We are going to use the dot product with the concept of projection. Projection: is putting one thing on another (defined by Me :) ) When two vectors a = OA and b = OB are placed tail to tail, and 0 is the angle between them, the scalar projection of a on b is ON. To solve for the scalar projection of a on b: from the dot product we know: a b = |a||b|cos 0 May 23­8:38 AM 1 Example 1: For the vectors a = (­3, 4, 5 3) and b = (­2, 2, ­1), calculate each of the following scalar projections: a) a on b b) b on a May 22­8:45 PM 2 Example 2: Determine the angle that the vector OP = (2, 1, 4) makes with each of the coordinate axis. May 23­8:45 AM 3 Example 3: Find the vector projection of OA = (4,3) on OB = (4, ­1). Homework p. 398­399 #5, 6, 7, 8a, 11, 14 May 22­8:53 PM 4 May 23­1:27 PM 5