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Vector lengths 1. Let A = �1, 2�, B = �1, −1� and C = i + 2j + 3k. Find the lengths of A, A + B and C. Answer: Length is just √ √ an expression of the Pythagorean theorem. The picture below shows |A| = 1 + 22 = 5 A 2 1 Likewise A + B = �2, 1� ⇒ |A + B| = have the same length. √ 5. Perhaps, it’s surprising that A and A + B can B A A+B C is a vector in space, but the length is computed the same way, except there are 3 terms under the radical sign. � √ |C| = 1 + 22 + 32 = 14. MIT OpenCourseWare http://ocw.mit.edu 18.02SC Multivariable Calculus Fall 2010 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.