Vector (cross) product
Practice Flashcards
Flip to reveal answersWhat does the cross product v×w give?
Track your progress — Sign up free to save your progress and get smart review reminders based on spaced repetition.
All 8 Flashcards — Vector (cross) product
Sign up free to track progress and get spaced-repetition review schedules.
Question
What does the cross product v×w give?
Answer
A VECTOR perpendicular to both v and w (the dot product gives a scalar).
Question
Component formula for v×w?
Answer
v×w = (v₂w₃ − v₃w₂, v₃w₁ − v₁w₃, v₁w₂ − v₂w₁).
Question
What does |v×w| equal?
Answer
|v×w| = |v||w| sin θ = the area of the parallelogram with sides v and w.
Question
Area of triangle ABC using vectors?
Answer
½|AB×AC| — two sides from the same vertex, crossed, length halved.
Question
How can you check a cross product is right?
Answer
It must be perpendicular to both inputs: v·(v×w) = 0 and w·(v×w) = 0.
Question
Dot product vs cross product — what comes out?
Answer
Dot → a scalar (number); cross → a vector.
Question
Is the cross product commutative?
Answer
No — w×v = −(v×w) (opposite direction); and v×v = 0.
Question
When is |v×w| = 0?
Answer
When v and w are parallel (sin θ = 0) — they span no area.
Read the notes
Full study notes for Vector (cross) product
Topic 3.13 hub
Scalar & vector products (HL only)
More from Topic 3.13
All flashcards in this topic
Math AI exam skills
Paper structures & tips
Track your progress with spaced repetition
Sign up free — Aimnova tells you exactly which cards to review and when, so you remember everything before your IB exam.
Start Free