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vectors - use whichever way is more convenient for the...

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Vectors The geometry of vectors shows up so much in physical systems, that it’s worth spending some time to gain facility at it. The addition and subtraction of vectors and the multiplica- tion of vectors by scalars are the most common processes that you use. The usual picture of a vector is a directed line segment. That is, a line with an arrow attached to indicate direction. The addition and subtraction of vectors in this picture follows just a few basic rules: The parallelogram law for addition and subtraction, and changing the length (and possibly reversing the direction) of the vector as you multiply it by a scalar. A A A B B 1.5 A -.5 A A + B B - A You can picture a vector by moving it around parallel to itself, and sometimes that makes it easier to look at these basic operations. The addition of vectors can as easily be pictured by placing the arrows tip-to-tail instead of the way shown in the first sketch. You

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Unformatted text preview: use whichever way is more convenient for the problem at hand. 1 2 Vectors Practice Set 1 [1] A B Draw the sum of the two vectors in the picture. [2] Draw the diﬀerence of the same two vectors, ~ A-~ B . [3] Draw 2 ~ A-~ B . [4] Draw-~ A + 2 ~ B . Vectors 3 Solutions for Practice Set 1 [1] Draw the sum of the two vectors in the picture. A B [2] Draw the diﬀerence of the same two vectors, ~ A-~ B . A B [3] Draw 2 ~ A-~ B . 2 A B A- B [4] Draw-~ A + 2 ~ B . 2 B B A- A 4 Vectors Practice Set 2 [1] C D Draw the sum of the two vectors in the picture. [2] Draw the diﬀerence of the same two vectors. [3] Draw 2 ~ C-~ D . [4] Draw-~ C + 2 ~ D . Vectors 5 Practice Set 3 [1] A B C Draw the sum of the three vectors in the picture. [2] Draw ~ A-~ B + ~ C . [3] Draw ~ B-~ A-~ C . [4] Draw ~ C-( ~ A + ~ B ) . [5] Draw 2 ~ A + 3 ~ B ....
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