The vector product in 3D
"The vector product in 3D" is a free, interactive Class 11 Physics simulation for NEET and JEE, built on the NCERT section "Vector product of two vectors" in System of Particles and Rotational Motion. Rotatable 3D view: a and b in a plane, a × b perpendicular with magnitude ab sin θ (area of the parallelogram); swapping order flips it. NEET has asked about this idea 2 times in 10 years of papers. JEE Main asked 66 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
From the lesson Vector product of two vectors in System of Particles and Rotational Motion. Change the values and watch what happens.
What it shows
NCERT §6.5
Rotatable 3D view: a and b in a plane, a × b perpendicular with magnitude ab sin θ (area of the parallelogram); swapping order flips it.
Controls
4 to try
- Dragtips of a and b
- Dragrotate camera
- Togglea × b / b × a
- Readoutcomponents and |c|
Try this
Make |a × b| equal to 12 with |a| = 4 and |b| = 6 (θ = 30° or 150°), then show b × a points the other way.
Common mistake
A × b = b × a.
In NEET
10 years of papers
Asked 2 times in 10 years of NEET.
See the past questions: Vector Algebra, System of Particles and Rotational Motion (chapter)
In JEE Main
42 shifts analysed
66 questions from System of Particles and Rotational Motion across the 42 JEE Main shifts Lumi has analysed (2017–2026).
The idea behind it
NCERT §6.5
- The vector (cross) product c = a × b has magnitude ab sin θ, where θ is the smaller angle between a and b, and points perpendicular to the plane of a and b.
- Direction by the right-hand rule: curl the fingers of the right hand from a to b through the smaller angle; the thumb gives c. A right-handed screw turned from a to b advances along c.
- The cross product is not commutative: b × a = −(a × b), same size, opposite direction. The scalar product is commutative.
- Under reflection every component changes sign, so a → −a and b → −b, but a × b is unchanged.
- Both products are distributive: a × (b + c) = a × b + a × c. Also a × a = 0.
- Unit vectors: i × i = j × j = k × k = 0; i × j = k, j × k = i, k × i = j, and the products in the reverse order are negative.
- In components, a × b = (a_y b_z − a_z b_y) i + (a_z b_x − a_x b_z) j + (a_x b_y − a_y b_x) k, which is the determinant with rows (i, j, k), (aₓ, a_y, a_z), (bₓ, b_y, b_z).
- For a = 3i − 4j + 5k and b = −2i + j − 3k: a · b = −25 and a × b = 7i − j − 5k, so b × a = −7i + j + 5k.
Questions
5 answers
- What does the "The vector product in 3D" simulation show?
- Rotatable 3D view: a and b in a plane, a × b perpendicular with magnitude ab sin θ (area of the parallelogram); swapping order flips it.
- What mistake does the "The vector product in 3D" simulation fix?
- A common mistake it clears up: A × b = b × a.
- Has NEET asked about this idea?
- Yes. NEET has asked about this idea 2 times in 10 years of papers.
- Does JEE Main ask questions from System of Particles and Rotational Motion?
- Yes. JEE Main asked 66 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
- Is this simulation free?
- Yes. It is free and runs in the browser on a phone or a laptop. It belongs to the lesson "Vector product of two vectors" in System of Particles and Rotational Motion (Class 11 Physics).
Embed this simulation
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