From Two Points to a Unit Vector
This animation walks through finding a unit vector between two points in 3D space. Starting with points P(1, -2, 4) and Q(3, 1, -2), it shows how to compute the displacement vector PQ by subtracting coordinates, then calculates its magnitude using the distance formula, and finally normalizes the vector by dividing each component by its length. Useful for students learning vector operations in precalculus 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 60-second educational math animation in a clean whiteboard style. Topic: From Two Points to a Unit Vector Given: P = (1, −2, 4) Q = (3, 1, −2) Show the calculation step by step: →PQ = Q − P = ⟨3−1, 1−(−2), −2−4⟩ = ⟨2, 3, −6⟩ Then: ‖PQ‖ = √(2² + 3² + (−6)²) = √49 = 7 Finally: u = →PQ / ‖PQ‖ = ⟨2/7, 3/7, −6/7⟩ Animate each equation progressively, with clear mathematical notation and smooth transitions. Use a simple academic whiteboard aesthetic. Highlight the final unit vector. Prioritize mathematical accuracy and readability. Do not change any numbers, signs, fractions, or notation.
Make the next one in this series
- Show how to find a unit vector in 2D using two points on a coordinate plane.
- Demonstrate how to find a vector parallel to PQ with a specific magnitude, like 10.
- Explain how to compute the dot product and angle between two 3D vectors.
