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
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