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" In this gure the vector R is called the vector sum of the two vectors of magnitudes 50 " and 75; that is, the single vector R is mathematically and geometrically equivalent to the " combined e ects of the two component vectors, so that R is called the vector sum of the two component vectors. From the gure, it s apparent that vector addition is quite di erent from the ordinary algebraic addition of scalar quantities. This can be investigated in more detail as follows. " Using the above gure, let A denote the displacement vector of magnitude 50, that is, " " " jAj 50, and let B denote the displacement vector of magnitude 75, jB j 75. " " " If we now let R be the combined e ect (the vector sum ) of A and B, we then nd by " direct experiment with displacements that the value of R can be found graphically by any of " the three equivalent procedures shown in Figs. 2-A, 3-A, and 4-A. Note that R has the same magnitude and direction in all three gures.

Don t use an instance variable when a local variable will work! Not only does this impact memory use, but it reduces the risk that an object slips out to some place it shouldn t be used, either accidentally or on purpose. Wait to declare a variable until just before it s used. And you should always initialize a local variable at the time it is declared (which is just before use), with the exception of try/catch blocks. In that case, if the variable is declared and assigned in the try/catch block, the compiler won t let you use it beyond that block, so if you need the variable after a try or catch block, then you ll have to declare it first outside the try/catch. Another way to reduce scope is to use a for loop rather than while. Remember from the Programmer s exam chapters that when you declare a variable as part of the for loop declaration (as opposed to merely initializing a variable declared prior to the loop), then the variable s scope ends with the loop. So you get scope granularity that s even smaller than a method.

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Objects are meant to have both state and behavior; they re not simply glorified structs. If you need a data structure, use a Collection. There are exceptions to this, however, that might apply to your exam assignment. Sometimes you do need an object whose sole purpose is to carry data from one location to another usually as a result of a database request. A row in a table, for example, should be represented as an object in your Java program, and it might not always need methods if its sole job is to be, say, displayed in a GUI table. This is known as the ValueObject pattern. Which brings us to the next issue.

In the gures, the vector quantities all represent distances measured o at di erent angles relative to some speci c reference line " In the gures, let us suppose that the distance represented by A happens to lie exactly " is at an angle of zero degrees with respect to along the reference line; that is, suppose that A the reference line; symbolically this can be shown by writing that " " A jAj=08 " Or, if A were measured (for example) at an angle of, say, 208 with respect to the reference line, this would be shown by writing " " A jAj=208 " " In Fig 2-A, B is a distance, of magnitude jBj, measured from point P at an angle let us " denote by b degrees relative to the vector A, as shown in the gure.

When you use familiar patterns, then you ve got a kind of shorthand for discussing your design with other programmers (even if that discussion is between your code/ comments and the other person. If you ve done it right, you won t personally be there to talk about it, as is the case with the Developer exam). If you need a Singleton, make a Singleton don t simply document that there is to be only one of these things. On the other hand, don t go forcing your design into a pattern just for the sake of using a pattern. Simplicity should be your first concern, but if it s a toss-up between your approach and an equally complex, well-known design pattern, go for the pattern.

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(We re assuming " is at 08 relative to the reference line) The resultant of these two measurements is a that A " distance of magnitude jRj at, let us say, an angle of r degrees relative to the reference line Algebraically, the whole operation can be expressed by writing that " " " jAj=08 jBj=b8 jRj=r8 " " " " or, in a more abbreviated form, A B R, which says that vector R is equal to the sum of " and B " vectors A " " " " Now, in regard to actually nding the value of R, where R A B, two procedures, one graphical and the other mathematical, are available Here we ll mainly emphasize the graphical procedure, as follows At the beginning of this discussion we de ned that quantities are truly vector quantities only if they obey the PARALLELOGRAM LAW OF ADDITION.

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