Casio fx-3650p and HP
21S: 3D Vectors: Dot Products and Angle
The
following program computes the dot product two three-dimension vectors and the
angle between them. Degrees mode is
set.
Casio fx-3650P
Input: [A, B, C] and [X, Y, D]
Program
(66 steps):
Deg
: ? → A : ? → B : ? → C :
? →
X : ? → Y : ? → D :
AX
+ BY + CD → M ◢
√ (
A^2 + B^2 + C^2 :
Ans
√ ( X^2 + Y^2 + D^2 :
cos^-1
( M ÷ Ans ◢
HP 21S
Input: [R1, R2, R3] and [R4, R5, R6]. Store the amounts before running the program
(XEQ B)
Program
(47 steps):
|
Step
|
Code
|
Key
|
Notes
|
|
01
|
61, 41, B
|
LBL B
|
Beginning
of program
|
|
02
|
61, 23
|
DEG
|
Set
degrees mode
|
|
03
|
22, 1
|
RCL 1
|
Calculate
dot product
|
|
04
|
55
|
*
|
|
|
05
|
22, 4
|
RCL 4
|
|
|
06
|
75
|
+
|
|
|
07
|
22, 2
|
RCL 2
|
|
|
08
|
55
|
*
|
|
|
09
|
22, 5
|
RCL 5
|
|
|
10
|
75
|
+
|
|
|
11
|
22, 3
|
RCL 3
|
|
|
12
|
55
|
*
|
|
|
13
|
22, 6
|
RCL 6
|
|
|
14
|
74
|
=
|
|
|
15
|
21, 0
|
STO 0
|
|
|
16
|
26
|
R/S
|
Display
dot product
|
|
17
|
22, 1
|
RCL 1
|
Calculate
angle
|
|
18
|
51, 11
|
x^2
|
|
|
19
|
75
|
+
|
|
|
20
|
22, 2
|
RCL 2
|
|
|
21
|
51, 11
|
x^2
|
|
|
22
|
75
|
+
|
|
|
23
|
22, 3
|
RCL 3
|
|
|
24
|
51, 11
|
x^2
|
|
|
25
|
74
|
=
|
|
|
26
|
11
|
√
|
|
|
27
|
74
|
=
|
|
|
28
|
22, 4
|
RCL 4
|
|
|
29
|
51, 11
|
x^2
|
|
|
30
|
75
|
+
|
|
|
31
|
22, 5
|
RCL 5
|
|
|
32
|
51, 11
|
x^2
|
|
|
33
|
75
|
+
|
|
|
34
|
22, 6
|
RCL 6
|
|
|
35
|
51, 11
|
x^2
|
|
|
36
|
34
|
)
|
|
|
37
|
11
|
√
|
|
|
38
|
55
|
*
|
|
|
39
|
51, 74
|
LAST
|
|
|
40
|
74
|
=
|
|
|
41
|
22, 0
|
RCL 0
|
|
|
42
|
45
|
÷
|
|
|
43
|
51, 74
|
LAST
|
|
|
44
|
74
|
=
|
|
|
45
|
51, 24
|
ACOS
|
|
|
46
|
21, 7
|
STO 7
|
|
|
47
|
61, 26
|
RTN
|
End
program
|
The
key strokes for the HP 20S is similar.
Example: [1, -2, 4]; [3, 7, 6]
Results:
Dot
= 13
Angle
= 72.98650490190°
Eddie
This
blog is property of Edward Shore, 2017
