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12 Nov 2019
True or False. Circle your answer. (a) T F: For any u, v belongsto R^3, the set {cu + dv: c, d belongsto R} fills out the plane through u and v. (b) T F: If the set of all linear combinations of {u, v} is a line through origin, then the set of all linear combinations of {au, bv} is also a line through origin, where a, b are any non-zero scalars. (c) T F: If u and v are unit vectors, then the minimum possible value of |u middot v| = 1. (d) T F: If ||u|| = 0, then u must be a zero vector. (e) T F: For any non-zero vectors u and v, the value of |u middot v| is minimum when they are perpendicular to each other.
True or False. Circle your answer. (a) T F: For any u, v belongsto R^3, the set {cu + dv: c, d belongsto R} fills out the plane through u and v. (b) T F: If the set of all linear combinations of {u, v} is a line through origin, then the set of all linear combinations of {au, bv} is also a line through origin, where a, b are any non-zero scalars. (c) T F: If u and v are unit vectors, then the minimum possible value of |u middot v| = 1. (d) T F: If ||u|| = 0, then u must be a zero vector. (e) T F: For any non-zero vectors u and v, the value of |u middot v| is minimum when they are perpendicular to each other.
Beverley SmithLv2
26 Jan 2019