From Two Points to a Unit Vector
This animation shows how to build a vector from two points in space, find its length, and normalize it into a unit vector. Starting with points P and Q, it demonstrates subtracting coordinates to get the displacement vector, computing its magnitude using the distance formula, then dividing each component by that magnitude to produce a vector of length one. Useful for students learning vector operations in multivariable calculus or introductory linear algebra courses.
Narrated · 16:9 · Preview before teaching · automatic layout checks do not establish subject accuracy
The prompt that made it
Create a 40-second university-level mathematics educational animation. TITLE: From Two Points to a Unit Vector STYLE: Clean, professional mathematical whiteboard/lightboard animation. Minimal design. No characters. No avatars. No stock footage. No decorative graphics. No AI-generated introduction. IMPORTANT: The narration below is FINAL. Use it exactly as written. Do not paraphrase, rewrite, shorten, expand, or add narration. The visuals must follow the narration exactly. NARRATION: "Two points in space. I want three things from them: the arrow that runs between them, how long it is, and a version of that arrow exactly one unit long. P is one, negative two, four. Q is three, one, negative two. To get the vector from P to Q, subtract the tail from the head. Three minus one is two. One minus negative two is three. Negative two minus four is negative six." VISUAL SEQUENCE: INTRO: Start with a blank whiteboard. Write: From Two Points to a Unit Vector Then show: P → Q: components, length, direction Do not add any other explanatory text. STEP 1 — COMPONENT FORM: Show: P = (1, −2, 4) Q = (3, 1, −2) Then show: →PQ = Q − P Then progressively write: →PQ = ⟨3 − 1, 1 − (−2), −2 − 4⟩ Keep P and Q visible. STEP 2 — COMPONENT CALCULATION: Synchronize the writing with the narration. When the narration says: "Three minus one is two." Show: 3 − 1 = 2 When the narration says: "One minus negative two is three." Show: 1 − (−2) = 3 Highlight this calculation in BLUE. When the narration says: "Negative two minus four is negative six." Show: −2 − 4 = −6 Then show the completed result: →PQ = ⟨2, 3, −6⟩ Hold the completed vector briefly at the end. COLOR SYSTEM: BLACK: Normal mathematical calculations and working. BLUE: Annotations and emphasis. RED: Reserved for final answers. MATHEMATICAL ACCURACY IS CRITICAL. Preserve exactly: P = (1, −2, 4) Q = (3, 1, −2) →PQ = Q − P →PQ = ⟨3 − 1, 1 − (−2), −2 − 4⟩ →PQ = ⟨2, 3, −6⟩ Do not change numbers or signs. Do not invent additional mathematical steps. Do not add explanations that are not present in the narration. The video should look like a professionally produced university mathematics lesson, with the mathematics appearing progressively in sync with the spoken narration.
Make the next one in this series
- Show how to compute the magnitude of a 3D vector using the distance formula
- Explain why dividing a vector by its magnitude always yields a unit vector
- Demonstrate finding a unit vector in the direction of a given vector
