How to do vectors (scalar product, cross product, angle) on the Casio fx-CG50
Magnitude, scalar (dot) product, vector (cross) product and the angle between two vectors. Exact keystrokes for the fx-CG50 first, then the other calculators, a worked example you can check your answers against, the mistakes that cost marks, and the same thing in Desmos.
When you need it
A Level Maths: magnitudes, unit vectors and position vectors in 2D and 3D; Further Maths: the scalar product, lines and planes, and the vector product.
Practise it: Vectors.
Keystrokes on your calculator
Pick your calculator: the page remembers it next time.
Vectors on the Casio fx-CG50
Written for OS 3.80 (menus unchanged from OS 3.60 onwards as far as we can tell). Casio fx-CG50: graphic (GDC).
- Vectors work in RUN-MATRIX: F3 (MAT/VCT), then F6 (M⇔V) to switch to the vector list. Set Vct A to dimension 3 and enter 2, −1, 3; Vct B = 1, 4, −2.
- OPTN F2 (MAT/VCT), then the vector commands (DotP, CrossP, Angle, UnitV, Norm) on the next page (F6 ▷): DotP(Vct A, Vct B), CrossP(Vct A, Vct B), Norm(Vct A).
- Angle: Angle(Vct A, Vct B) in the current angle mode, or cos⁻¹(DotP(Vct A, Vct B) ÷ (Norm(Vct A) × Norm(Vct B))).
- Without the vector menu (older OS): store the vectors as lists {2, −1, 3} → List 1 and {1, 4, −2} → List 2, then Sum(List 1 × List 2) is the dot product (OPTN F1 (LIST) → Sum).
- The vector functions were added to the fx-CG50 in the OS 3.x updates; if your menu does not show them, update the OS or use the list method.
Vectors on the TI-84 Plus CE
Written for OS 5.8.x. TI-84 Plus CE: graphic (GDC); also the TI-84 Plus CE Python / CE-T Python Edition.
- The TI-84 Plus CE has no vector commands. Store the vectors as lists: {2, −1, 3} sto→ L1, {1, 4, −2} sto→ L2.
- Dot product: sum(L1*L2) (sum( is in 2nd stat → MATH).
- Magnitude: √(sum(L1²)). Angle: cos⁻¹(sum(L1*L2) ÷ (√(sum(L1²))·√(sum(L2²)))) in DEGREE mode.
- Cross product: work out the components with the formula (a₂b₃ − a₃b₂, a₃b₁ − a₁b₃, a₁b₂ − a₂b₁).
Vectors on the TI-Nspire CX II
Written for OS 6.x. TI-Nspire CX II: graphic (GDC), non-CAS; the CX II CAS is not allowed in IB, A Level or IGCSE exams.
- Calculator page: a:=[2,−1,3] and b:=[1,4,−2].
- dotP(a,b), crossP(a,b), norm(a) (menu → Matrix & Vector → Vector).
- Angle: cos⁻¹(dotP(a,b)/(norm(a)·norm(b))) in degree mode (or convert).
Vectors on the Casio fx-991EX ClassWiz
Written for the fixed ROM (these models take no OS updates). Casio fx-991EX ClassWiz: scientific (no graphs).
- MENU 5 (Vector). Define VctA with 3 dimensions: 2, −1, 3. Define VctB: 1, 4, −2. AC.
- Dot product: VctA, OPTN → Dot Product, VctB, =.
- Cross product: VctA × VctB =. Magnitude: Abs(VctA) with SHIFT hyp.
- Angle: OPTN → Angle(VctA, VctB).
Vectors on the Casio fx-991CW ClassWiz
Written for the fixed ROM (these models take no OS updates). Casio fx-991CW ClassWiz: scientific (no graphs); the newer ClassWiz with a HOME menu of apps.
- HOME → Vector. Define VctA and VctB (3 dimensions).
- Use Dot Product, Angle and Unit Vector from CATALOG → Vector; VctA × VctB for the cross product.
Worked example
a = (2, −1, 3), b = (1, 4, −2). Find a · b, a × b, |a| and the angle between a and b.
Answers (checked with Python)
a · b = −8, a × b = (−10, 7, 9), |a| = √14 = 3.74166, angle = 117.8°.
Common calculator mistakes
- The angle between two lines uses their direction vectors; if the answer is obtuse the acute angle between the lines is 180° − θ.
- Degree vs radian mode for the angle.
- Using position vectors instead of direction vectors (AB = b − a).
- Cross product order: a × b = −(b × a).
Do it in Desmos
Not in the exam. Desmos is not allowed in A Level exams. Use it to learn, to check a calculator answer, and to see what a function or data set looks like.
- Store the vectors as lists: a = [2, −1, 3], b = [1, 4, −2].
- total(a·b) is the dot product; √(total(a²)) the magnitude.
- The angle: arccos(total(a·b)/(√total(a²)√total(b²))) (switch Desmos to degrees in the wrench menu).
- For 3D pictures use the Desmos 3D calculator (desmos.com/3d).
The interactive graph loads here when you scroll to it.
Or open desmos.com/calculator and type:
a=[2,-1,3]b=[1,4,-2]total(ab)√{total(a^{2})}arccos(frac{total(ab)}{√{total(a^{2})}√{total(b^{2})}})
More calculator skills
Sources
- Casio fx-CG50 Software User's Guide, OS 3.70 (PDF) : Casio fx-CG50, OS 3.80 (menus unchanged from OS 3.60 onwards as far as we can tell).
- TI-84 Plus CE guidebook (Texas Instruments) : TI-84 Plus CE, OS 5.8.x.
- TI-Nspire CX II guidebooks (Texas Instruments) : TI-Nspire CX II, OS 6.x.
- Casio fx-991EX / fx-570EX Quick Start Guides : Casio fx-991EX ClassWiz, the fixed ROM (these models take no OS updates).
- Casio fx-991CW / fx-570CW User's Guide : Casio fx-991CW ClassWiz, the fixed ROM (these models take no OS updates).
- Desmos Help Center for the Desmos functions.
Menu names are taken from each manufacturer's manual for the OS versions shown. Menus can move slightly between OS updates: if a screen looks different on yours, the manual for your version is the reference, and please tell us so we can update this page. Worked-example answers were recomputed independently in Python.