IB Maths: Vectors Revision | AI Study Method

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What does a vector have?

Vectors is a core part of IB Maths. Revise the key concepts and common mistakes below, then lock them in with the free games.

Key concepts

Line equationr = a + λb, point a, direction b.

Plane (vector)r·n = d, n is the normal vector.

Plane (cartesian)n1 x + n2 y + n3 z = d.

Point to planeDistance = |n·p - d| / |n|.

Skew linesNon-parallel lines that do not intersect.

Direction vectorVector along the line's direction.

Cross producta × b yields vector perpendicular to a and b.

Magnitude rule|a × b| = |a||b| sin θ.

Right-hand ruleCurl fingers from a to b, thumb is a × b.

Parallelogram areaArea = |a × b| of two-vector parallelogram.

Triangle areaTriangle = ½ |a × b|.

Parallel vectorsa × b = 0 when a ∥ b.

VectorQuantity with magnitude and direction.

Magnitude|a| = √(a1^2 + a2^2 + a3^2).

Learn Vectors step by step

Free interactive mini-lessons: short screens, worked examples and quick checks. Pick your exam board to open its course map, then tap L on this topic:

IB Mathematics: Analysis & Approaches · HL IB Mathematics: Analysis & Approaches · SL IB Mathematics: Applications & Interpretation · HL IB Mathematics: Applications & Interpretation · SL

Common mistakes to avoid

Questions where students often pick the tempting wrong answer — make sure you know the right one:

What does a vector have?✗ Only a size (magnitude). ✓ Both magnitude and direction.

What is the resultant of two vectors?✗ The difference of their sizes only. ✓ The single vector with the same overall effect (tip-to-tail).

Practise Vectors — free games

Test yourself with these quick revision games for this topic:

▶ Two Truths, One Lie ▶ Reveal Race ▶ Connections Grid ▶ Falling Words ▶ Word Web

See all 22 games in the Revision Arcade →

Vectors

Key concepts

Common mistakes to avoid

Practise Vectors — free games

More IB Maths topics