How to do vectors (scalar product, cross product, angle) on the Casio fx-CG50, TI-84 Plus CE and TI-Nspire CX II
On the fx-CG50: F3 (MAT/VCT) → F6 (M⇔V) → OPTN → F2 (MAT/VCT) (not in IB Examination Mode).On the TI-84 Plus CE: dot product sum(L1*L2), with sum( from 2nd stat → MATH.On the TI-Nspire CX II: menu → Matrix & Vector → Vector.
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 HL and AI HL (vectors are not in the SL syllabus of either course): the angle between vectors or lines, the scalar and vector products, and (AA HL) planes. Most AA vector questions need exact working, so use the calculator to check or for the final angle.
Practise it: HL AA 3D vectors · HL AA vector lines · HL AA planes · HL AI 3D vectors.
Which IB course and paper
| Course | GDC papers | What you use it for |
|---|---|---|
| AA SL | Not in the syllabus | — |
| AA HL | Papers 2 and 3 (Paper 1 is calculator-free) | Scalar and vector products, angles, lines and planes. Many vector questions want exact working: use the GDC to check. |
| AI SL | Not in the syllabus | — |
| AI HL | Papers 1, 2 and 3 | Scalar and vector products, angles between vectors, and vector kinematics. |
A GDC is allowed on every AI paper and on AA Papers 2 and 3; AA Paper 1 is calculator-free, so learn the method by hand as well.
Topic notes: 3D vectors (AI HL) · Vector equations of lines in 2D and 3D (AI HL) · 3D vectors (AA HL) · Lines and planes in 3D (AA HL).
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).
Not in the IB exam. Casio lists vector calculations among the functions its IB Examination Mode turns off, so these vector commands will not be there in Paper 2 or 3. Learn to work out the scalar product, vector product, magnitude and angle by hand, and use the steps below to check your practice answers.
Watch the key presses on the fx-CG5010 presses, one at a time
The walkthrough needs JavaScript. The same key presses are in the numbered steps below.
- 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.
Watch the key presses on the TI-84 Plus CE5 presses, one at a time
The walkthrough needs JavaScript. The same key presses are in the numbered steps below.
- 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 a different model: check the exam rules before using one).
- 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).
For teachers: Show on the board Print a keystroke card Teaching GDC skills
Quick answers
How do I find a cross product on the fx-CG50?
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).
Not in the IB exam. Casio lists vector calculations among the functions its IB Examination Mode turns off, so these vector commands will not be there in Paper 2 or 3. Learn to work out the scalar product, vector product, magnitude and angle by hand, and use the steps below to check your practice answers.
How do I find a cross product on the TI-84 Plus CE?
The TI-84 Plus CE has no vector commands. Store the vectors as lists: {2, −1, 3} sto→ L1, {1, 4, −2} sto→ L2. Cross product: work out the components with the formula (a₂b₃ − a₃b₂, a₃b₁ − a₁b₃, a₁b₂ − a₂b₁).
How do I find a cross product on the TI-Nspire CX II?
Calculator page: a:=[2,−1,3] and b:=[1,4,−2]. dotP(a,b), crossP(a,b), norm(a) (menu → Matrix & Vector → Vector).
How do I do a dot product on the TI-84 Plus CE?
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).
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°.
Now try it on an exam-style question
Use the keystrokes above on IB-style vector lines questions. Free to try, no sign-up.
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).
- Angle mode: calculus with trig functions (and most AA trig) needs radians; bearings and triangle questions use degrees. Check the mode before the first trig question of the paper.
- Accuracy: unless the question says otherwise, IB markschemes want answers exact or to 3 significant figures. Keep the full calculator value for later parts and round only the answer you write down (x = 2.094551… is written 2.09, not 2.1 or 2.0946).
If you get an error
fx-CG50: Ma ERROR
Ma ERROR Casio's Math ERROR: the result is outside the allowable calculation range, or you are trying to do an illegal mathematical operation, such as dividing by zero. Check: Look for a zero denominator, sin⁻¹ or cos⁻¹ of a number bigger than 1 (often a wrong side or angle in the sine or cosine rule), the log of 0 or of a negative number, and a value stored in a variable earlier that you forgot about. Fix: Casio's advice: check your input values and change them so the result is within the allowable range.
TI-84 Plus CE: ERR:DOMAIN, ERR:DIM MISMATCH, ERR:SYNTAX
ERR:DOMAIN A value given to a function or instruction is outside the values it accepts. In a regression, TI says it means the data do not suit the model you chose. Check: Is every input allowed? σ must be positive, p between 0 and 1, and sin⁻¹ or cos⁻¹ needs a number from −1 to 1. Exponential and power models need positive data. Fix: Change the value that is out of range, or choose a model that suits the data.
ERR:DIM MISMATCH Lists or matrices in the same operation have different sizes (TI's example: multiplying two lists with different numbers of elements). Check: L1 and L2 with different numbers of values (one value missed or typed twice), a frequency list of the wrong length, or matrices whose sizes cannot be multiplied. Fix: Make the lists the same length, or check the size of each matrix.
ERR:SYNTAX The command contains a syntax error: a misplaced function, argument, bracket or comma. Check: TI points out that subtract − and negative (−) are different keys, and using the wrong one causes this error. Then check the brackets and commas. Fix: Find the misplaced function, argument, bracket or comma and correct it.
TI-Nspire CX II: Domain error, Dimension mismatch, Syntax error
Domain error An argument must be in a specified domain, and this one is not (TI's example: rand(0)). Check: Is every input allowed? σ must be positive, p between 0 and 1, and sin⁻¹ or cos⁻¹ needs a number from −1 to 1. Fix: Change the value that is out of range.
Dimension mismatch Two or more arguments must have the same dimension and do not (TI's example: [1,2]+[1,2,3]). Check: Lists of different lengths in a statistics command, or vectors or matrices of different sizes. Fix: Make the lists, vectors or matrices the sizes the operation needs.
Syntax error The syntax checker found a problem. Check: A missing bracket or comma. Fix: Correct the expression and try again.
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).
Open desmos.com/calculator (free, in any browser) 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})}})
Questions
Can I use a calculator for vectors in the exam?
In IB Maths you can use one approved GDC on every AI paper and on AA Papers 2 and 3, in exam mode. AA Paper 1 is calculator-free, so learn the method by hand as well. Casio lists vector calculations among the functions its IB Examination Mode turns off, so these vector commands will not be there in Paper 2 or 3. Learn to work out the scalar product, vector product, magnitude and angle by hand, and use the steps below to check your practice answers.
What are the fx-CG50 keystrokes for vectors?
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. Then 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). Then 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))). The full steps and the other calculators are in the keystrokes section above.
Does this work on other calculators?
Yes. This page has keystrokes for the Casio fx-CG50, TI-84 Plus CE and TI-Nspire CX II. The worked example has the same answers on every model, so use it to check.
What should I write as working?
Write the maths, not the key presses: say what you are finding in normal notation (the equation, the probability statement or the integral), then the calculator's answer exact or to 3 significant figures unless the question says otherwise. Keep full accuracy in later parts.
How do I find a cross product on the fx-CG50?
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).
How do I find a cross product on the TI-84 Plus CE?
The TI-84 Plus CE has no vector commands. Store the vectors as lists: {2, −1, 3} sto→ L1, {1, 4, −2} sto→ L2. Cross product: work out the components with the formula (a₂b₃ − a₃b₂, a₃b₁ − a₁b₃, a₁b₂ − a₂b₁).
How do I find a cross product on the TI-Nspire CX II?
Calculator page: a:=[2,−1,3] and b:=[1,4,−2]. dotP(a,b), crossP(a,b), norm(a) (menu → Matrix & Vector → Vector).
How do I do a dot product on the TI-84 Plus CE?
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).
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 models 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. A calculator with no tab here has no checked steps for this skill yet. Worked-example answers were recomputed independently in Python.