Dot Product
a . b = |a||b| cos theta; the sign tells whether vectors point the same way.
Decision · step 2 of 4Plane Geometry: Points, a vector and a distance
Distance: the segment is the hypotenuse of a right triangle with legs 4 and 3, so the squared length is 4^2 + 3^2 = 25 and the length is sqrt(25), about 5. Comparing squared distances avoids the square root and stays exact in integers.
What you will see
One vector's shadow on the other.
Cost
| Space | O(1) |
|---|
How you work with it here
play it through, step one change at a time, scrub to any step, run it on your own input, try operations in any order.
Screen readers: Points announce coordinates and role; each step announces the geometric test and its result in words (left turn, intersects).
Reduced motion: Shapes appear in place; the sweep line jumps between events.
Before this
Related
Taught by the same lesson
Plane Geometry covers these too, in the same run.