Trident Help

Natural Scientific 991 manual · Chapter 11 of 18

Vectors

Define 2D and 3D vectors, add them, take dot and cross products and find their length.

11.1Define a vector#

Press MENU then 5 to open the Vector app (VCT). Press OPTN, choose 1 (Define Vector), pick VctA to VctD, choose the dimension (1:2 Elements or 2:3 Elements), and fill in the form pressing = after each element.

Example 11.1

Define VctA = (1, 2, 3)

  1. Open Vector and define VctA: OPTN 1, VctA, then 2 for three elements.

    MENU5OPTN1121=2=3=

  2. Insert VctA with OPTN 3 and press equals.

    OPTN3=
Result of the example "Define VctA = (1, 2, 3)" The display shows: VctA / [[1 2 3]].
You should see[[1 2 3]]
The Vector OPTN menu The display shows: 1:Define Vector / 2:Edit Vector / 3:VctA / 4:VctB.
The Vector OPTN menu

11.2Add and scale vectors#

Insert vectors with OPTN 3 to 6 (VctA to VctD), then use +, − and × as normal.

Example 11.2

Add two vectors

  1. Define VctA = (1,2,3) and VctB = (4,5,6).

    MENU5OPTN1121=2=3=OPTN1224=5=6=

  2. VctA + VctB.

    OPTN3+OPTN4=
Result of the example "Add two vectors" The display shows: VctA+VctB / [[5 7 9]].
You should see[[5 7 9]]
Example 11.3

Multiply by a number

  1. Define VctA, then VctA × 2.

    MENU5OPTN1121=2=3=OPTN3×2=
Result of the example "Multiply by a number" The display shows: VctA×2 / [[2 4 6]].
You should see[[2 4 6]]

11.3Dot product and cross product#

OPTN 8 is the dot product DotP( and OPTN 9 the cross product CrossP(. Separate the two vectors with a comma (SHIFT,)) and close the bracket. The cross product needs 3D vectors.

Example 11.4

Dot product

  1. Define VctA = (1,2,3), VctB = (4,5,6).

    MENU5OPTN1121=2=3=OPTN1224=5=6=

  2. DotP(VctA, VctB).

    OPTN8OPTN3SHIFT,)OPTN4)=
Result of the example "Dot product" The display shows: DotP(VctA,VctB) / 32.
You should see32
Example 11.5

Cross product

  1. Define the two vectors as before.

    MENU5OPTN1121=2=3=OPTN1224=5=6=

  2. CrossP(VctA, VctB).

    OPTN9OPTN3SHIFT,)OPTN4)=
Result of the example "Cross product" The display shows: CrossP(VctA,VctB) / [[-3 6 -3]].
You should see[[-3 6 -3]]
a⃗⋅b⃗=a1b1+a2b2+a3b3\vec a\cdot\vec b=a_1b_1+a_2b_2+a_3b_3
Dot product

11.4Find the length of a vector#

Use the absolute value key SHIFTAbshyp on a vector to get its length.

Example 11.6

Length of (3, 4)

  1. Define a two-element vector VctA = (3, 4): dimension key 1.

    MENU5OPTN1113=4=

  2. SHIFT hyp, VctA, bracket.

    SHIFTAbshypOPTN3)=
Result of the example "Length of (3, 4)" The display shows: Abs(VctA) / 5.
You should see5
Example 11.7

Length of (1, 2, 3) stays exact

  1. Define VctA = (1,2,3).

    MENU5OPTN1121=2=3=

  2. Abs(VctA).

    SHIFTAbshypOPTN3)=
Result of the example "Length of (1, 2, 3) stays exact" The display shows: Abs(VctA) / √14.
You should see√14
∣a⃗∣=a12+a22+a32|\vec a|=\sqrt{a_1^2+a_2^2+a_3^2}
Length of a vector

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