Wednesday, August 9, 2017

Casio fx-3650p and HP 21S: 3D Vectors: Dot Products and Angle

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