HP 35s User Manual

							 
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HP 35s  Working with vectors 
 
 
 
hp calculators 
 
 
 
 
HP 35s  Working with vectors 
 
 
 
 
Vectors 
 
Practice solving problems involving vectors 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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HP 35s  Working with vectors 
 
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Vectors 
 
From a mathematical point of view, a vector is an array of 2 or more elements arranged into a row or a column. Physical 
vectors that have two or three components and can be used to represent physical quantities such as position, velocity, 
acceleration, forces, moments, linear and angular momentum, angular velocity and acceleration, etc. 
 
On the HP 35s, vectors are entered using the !3 keystrokes. This opens an empty set of brackets to hold the 
values within the two dimensional or three dimensional vector. Elements of a vector are separated with a comma, which 
is entered by pressing #. The elements that can be stored in a vector cannot be complex numbers or vectors 
themselves. Vectors can also be used in equations. 
 
The HP 35s can add, subtract, multiply or divide vectors. The HP 35s can also compute the magnitude of a vector using 
the !$function.  
 
Vectors can also be used to pack real numbers into a register to increase the storage capacity of the HP 35s (or to store 
the same amount of information using less space). See the separate learning module for the indirect register data 
packing program for more information. 
 
To construct a vector in an equation or within a program that is composed of values found in stack or data registers, see 
page 10-8 of the HP 35s User’s Guide.  
Practice solving problems involving vectors  
Example 1: Perform this vector addition: [ 1 , 3 ] + [ 5 , 1 ]  
Solution: In RPN mode: !3%#&!3(#%) 
*
*In algebraic mode: !3%#&+)!3(#%* 
 Figure 1 
  
Answer: [ 6 , 4 ]. Figure 1 shows the answer in RPN mode. 
 
Example 2: Multiply the vector [ 1 , 3 ] by the scalar of 5  
Solution: In RPN mode: !3%#&(, 
*
*In algebraic mode: !3%#&+,(* 
 Figure 2 
  
Answer: [ 5 , 15 ]. Figure 2 shows the answer in RPN mode.   
						

							 
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HP 35s  Working with vectors 
 
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Example 3: Determine the magnitude of the vector [ 1 , 3 ].  
Solution: In RPN mode: !3%#&!$ 
*
*In algebraic mode: !$!3%#&* 
 Figure 3 
  
Answer: The magnitude is approximately 3.16, which is the length of the hypotenuse of the right triangle with sides 
of length 1 and 3. Figure 3 shows the answer in RPN mode. 
 
Example 4: Determine the dot product of [ 1 , 3 ] and  [ 3 , 1 ]  
Solution: In RPN mode: !3%#&!3&#%, 
*
*In algebraic mode: !3%#&,!3&#%* 
 Figure 4 
  
Answer: The dot product is equal to 6. Figure 4 shows the answer in RPN mode. 
 
Example 5: Construct a 3-D vector that contains the elements found in variables A, B, and C within a program.  
Solution: In either mode: !-.!3/0#/1#/2  
 Figure 5 
  
Answer: Figure 5 shows the resulting program line. This line will properly create the vector for further use.  
 
   
						

							 
 
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HP 35s  Writing a Simple Program 
 
 
 
 
Programming the HP 35s 
 
Practice example: the area of a circle 
 
Tools for programming 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
   
						

							 
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HP 35s  Writing a Simple Program 
 
hp calculators - 2 - HP 35s  Writing a Simple Program - Version 1.0 
Programming the HP 35s 
 
Doing a simple calculation once on the HP 35s is easy. Doing the same calculation many times, or doing a complicated 
calculation, takes longer. It can be better to store all the steps needed for the calculation in a program. A program is a 
set of instructions, stored all together. Once it is written, it can be tested to see if it works correctly. Then it can be used 
many times, without the need to press every key of the calculation each time. 
 
A simple program is just a set of keystrokes stored so that they can be carried out with one key. The HP 35s provides 
many commands to let programs do more, for example stop and ask for input, or show an intermediate result. This 
training aid concentrates on simple programming; it also shows a few of the more advanced programming commands. 
 
Practice example: the area of a circle 
 
Given “r” the radius of a circle, the circle’s area “A” is calculated from the formula A = ! r ². For example to calculate the 
area of a circle with radius 3cm, the following keys are pressed. 
 
In RPN mode:  !#$%& 
 
And in algebraic mode: #!&$%( 
 
 Figure 1 
 
Repeating the same 6 keys in RPN mode or 8 keys in algebraic mode for many circles is a lot of work. Here is how a 
program would make it easier. 
 
Example 1: Write a program in RPN mode to calculate the area of a circle, given its radius r. 
 
Solution: An RPN program and an algebraic program are shown below. The RPN program is shown first, called “A” 
for “Area”. 
 
  In RPN mode, type the same keys for calculating the area as before, but mark the beginning of the 
program with a label and the end of the program with a return. 
 
 First set program mode by typing ) and then go to the top of program memory (called PRGM 
TOP, see Figure 2), ready to begin a new program, by typing *++. Now the program can be 
typed: 
 
,-#$%&$. 
 
 The letter A is on the keyboard, below and to the right of the / key. Whenever , is typed, the  
 HP 35s uses the keys with the letters A – Z marked next to them to enter those letters.   
						

							 
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HP 35s  Writing a Simple Program 
 
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The program will look as shown in Figures 2 through 4 below. 
 
 Figure 2 
 
 Figure 3 
 
 Figure 4 
 
 Each line of the program begins with the letter of the label, and then has a four-digit line number. The rest 
of the program line is a function or a program instruction. The program instructions are LBL A and RTN, the 
functions are x ², ! and !.  
 
To use the program, it is necessary to move out of program mode, and to return to the beginning of the 
program. Then a radius is typed and the / key is pressed. The HP 35s executes (or runs) the program. 
 
To calculate the area of a circle with radius 5, make sure RPN mode is set, then press: 
 
)$.0/ 
 
 Figure 5 
 
Answer:  The area of a circle with radius 5 cm is just over 78.54 square cm. 
 
To calculate the area of another circle with a different radius, it is enough to type the new radius and press 
/ again. The program works like a new function, executed by means of the / key instead of a key 
with the name of one of the functions built into the HP 35s. 
 
Example 2: Write a program in algebraic mode to calculate the area of a circle, given its radius r. 
 
Solution:  In algebraic mode, the program looks very similar, but with the calculation keys typed in algebraic order. 
The HP 35s does not allow more than one program to have the same label, so the algebraic program 
below is given the label B. 
 
 Go to the beginning of program memory by typing *++ and set program mode by typing 
). Then type the algebraic mode program: 
 
 ,192#34(&%($. 
 
To get 1 press the * key; it has a small B to its lower right. The program lines are as listed below.   
						

							 
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HP 35s  Writing a Simple Program 
 
hp calculators - 4 - HP 35s  Writing a Simple Program - Version 1.0 
 
 
 Figure 6 
 
 Figure 7 
 
 Figure 8 
 
 Figure 9 
 
The second line is an instruction to set algebraic mode, to make sure program B is not used accidentally in 
RPN mode. If the user always works in algebraic mode, or always remembers to switch to the right mode 
before using a program then this program line is not needed, but it is always safer to use it. A similar line, 
setting RPN mode, could have been used in program A for the same reason. 
 
Line B003 squares the value in the X register, referred to in the program as REGX. This value will be the 
value keyed in before the program is run. 
 
This program works just like the RPN version. To use it, first move out of program mode, and to go to the 
beginning of the program. Then a radius is typed and the program is executed. 
 
Therefore, to calculate the area of a circle with radius 5, press: 
 
)$.0/ 
 
 Figure 10 
 
Answer: As in RPN mode, the area of a circle with radius 5 cm is calculated at just over 78.54 square cm. 
 
To calculate the area of another circle with a different radius, it is enough to type the new radius and press 
/ again. Like the RPN program, this program works similarly to a new function, executed by means of 
the / key instead of a key with the name of one of the functions built into the HP 35s. 
 
Tools for programming 
 
The HP 35s allows the user to create any or all of the labels from LBL A through LBL Z. The lines after a label all have 
that label at the beginning of their line numbers. When a new label is typed, the HP 35s starts over again at line 1, with   
						

							 
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HP 35s  Writing a Simple Program 
 
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the new label’s name at the beginning of each line. Figure 7 shows an example of this; if both program A and program B 
were typed, then after the RTN in program B, the first line of program A is displayed on the calculator screen. 
 
 Figure 11  
Each label can be used only one time, and the HP 35s treats the lines from one label until the next label as a separate 
program. It is also possible to have a program with no label, from the “PRGM TOP” until the first label.  
 
To list the programs in the HP 35s, press the keys $5 to get the “Memory” menu, and then 6 to get a display 
of programs. If the algebraic version of the circle program has been entered then the calculator screen will look like 
Figure 12. If only program A was typed, the screen will be as in Figure 13. 
 
 Figure 12 
 
This means that the program with label B is the first program in memory, and that it is 25 bytes long. A byte is a piece of 
calculator memory made up of 8 bits, and a bit is the smallest piece of memory, a single “0” or “1”. The HP 35s has more 
than 29,000 bytes of memory available to hold programs and equations entered by the user. Given this much memory, a 
long program could have up to 999 program lines, and that is why program line numbers are 3 digits long. The up and 
down arrows at the right of the screen mean that there are more programs in the calculator – information about each 
program in turn is displayed if the up or down arrow keys are pressed. If both the programs A and B have been entered, 
press 7 to see information about program A. 
 
 Figure 13 
 
Another tool to help in writing programs is the program checksum. To see the checksum for program A, press 
$8. While the 8 key is held down, the calculator will show: 
 
 Figure 14 
 
CK=DAF1means that the checksum for program A is the hexadecimal number DAF1. (The checksum for program B is 
AD0A.) If the program was not typed correctly, then the checksum will be different. Press the key labeled 9 at the 
bottom left of the keyboard to cancel the display of information about programs. 
 
The checksum has several purposes: 
 
 If a program is correctly copied to the HP 35s from a web page or a book – the HP 35s manual has many useful 
example programs – then the checksum on the HP 35s will be the same as the checksum given with the 
program. If the checksum is not the same, a mistake was made and the program should be checked and 
corrected before it is used. 
   
						

							 
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 If a user creates a new program on an HP 35s and then writes it down for future use, it is worth keeping a note 
of the checksum with the written program. That way, the program can be checked if it is typed into the HP 35s 
again later. 
 
 If a user wants to offer a program to other users, the checksum should be given with the program, so the other 
users can check if they have entered the program correctly into their HP 35s. 
 
The checksum can be very helpful, but it does not have to be used – for short programs such as the above it can be 
enough to step through the program with the up and down arrow keys and correct any mistakes. 
 
Mistakes can be either wrongly typed lines, or missing lines. To add a missing line, use the : and 7 keys until the 
line before the missing line is at the bottom of the screen. Then type the missing line or lines. If a line is wrong, move it to 
the lower line of the screen and use the ; key to delete one or more lines, then type the correct line or lines. 
 
Even after all typing errors have been corrected, a program can still be wrong if it was designed wrongly. The HP 35s 
manual provides advice on program testing and describes more programming tools. 
 
To go to a line in a program, to see it or to change it, use the GTO command, followed by a dot and then the program 
name and the line number. For example to go to line 5 of program A type *+-