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
AA SL/HL and AI HL: the angle between vectors or lines, the scalar product, and (HL) the vector product, planes and areas. Most AA vector questions need exact working, so use the calculator to check or for the final angle.
Practise it: SL AA vectors · HL AA vector lines · HL AA planes · HL AI 3D 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).
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 an approved calculator for IB exams, so never rely on it for Paper 2. It is excellent for learning, checking a GDC answer and building graphs for your Internal Assessment (IA).
- 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.
- 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.