Vector Commands

Number Theory and Algebra

• Vector Commands
  • Absolute value of the vector
  • Building a two-dimensional vector
  • Building a three-dimensional vector
  • Decomposing a two-dimensional vector
  • Decomposing a three-dimensional vector

Source: HP 35s User's Guide HP part number F2215AA-90001
Source: HP 49g+ Advanced User's Reference Manual HP part number F2228-90010

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Vector Commands

A vector is an array of 2 or 3 elements arranged into a column. Examples are shown below:

v₂ = [a,b] = [1.5,-2.2]
v₃ = [a,b,x] = [-1,3,6]

Absolute value of the vector

Note:

The HP 35s cannot handle vectors with more than 3 dimensions.

For a vector

x⃗ = (x₁, x₂, …, x_n)

the magnitude is defined as

| x⃗ | = √( x₁² + x₂² + … + x_n² )

Example:

Absolute value of vector [1,-2,6] = 6.40

LINE	DATA	OPERATIONS	DISPLAY	REMARKS
1		CLEAR 4'Σ
2	xi	Σ+	i	Perform 2-3 for i=1,2,…,n
3		SUMS 4'Σx² x

Building a two-dimensional vector

Build a vector with the values of Register X and Y (→V2).

Example:

-2, -6 = [-6.00,-2.00]

LINE	DATA	OPERATIONS	DISPLAY	REMARKS
1	b	ENTER
2	a	MODE 4'ALG [] R↓		set ALG mode
3		1'X , R↓ 2'Y
4		MODE 5'RPN	v2	back to RPN mode

; XEQ 3 ENTER
LBL Z
  ABS
  CLx
  eqn '[LASTx,REGY]'
RTN

Building a three-dimensional vector

Build a vector with the values of Register X, Y and Z (→V3).

Example:

2, 6, 8 = [8.00,6.00,2.00]

LINE	DATA	OPERATIONS	DISPLAY	REMARKS
1	x	ENTER
2	b	ENTER
3	a	MODE 4'ALG [] R↓		set ALG mode
4		1'X , R↓ 2'Y
5		, R↓ 3'Z
6		MODE 5'RPN	v3	back to RPN mode

; XEQ 4 ENTER
LBL U
  ABS
  CLx
  eqn '[LASTx,REGY,REGZ]'
RTN

Decomposing a two-dimensional vector

Decompose a two-dimensional vector into its elements or components (V→).

Example:

[2,3] = 3.00, 2.00

LINE	DATA	OPERATIONS	DISPLAY	REMARKS
1	v2	ENTER [] 0
2		, 1 ×	b
3		x<>y [] 1
4		, 0 ×	a

; XEQ 5 ENTER
LBL V
  ABS
  CLx
  eqn 'LASTx*[0,1]'
  eqn 'LASTx*[1,0]'
RTN

Decomposing a three-dimensional vector

Decompose a three-dimensional vector into its elements or components (V→).

Example:

[1,-5,2] = 2.00, -5.00, 1.00

LINE	DATA	OPERATIONS	DISPLAY	REMARKS
1	v3	[] 0 ,
2		0 , 1 x<>y
3		×	x
4		LASTx [] 0
5		, 1 ,
6		0 x<>y ×	b
7		LASTx [] 1
8		, 0 ,
9		0 ×	a

; XEQ 6 ENTER
LBL W
  ABS
  CLx
  eqn 'LASTx*[0,0,1]'
  eqn 'LASTx*[0,1,0]'
  eqn 'LASTx*[1,0,0]'
RTN