Vector Distances Flashcards
How to find distance from point to line formula way
Vector product way
= p-a cross d modded
/ mod d
How to find coordinates and then distance point to 3d line
Find a general point where perpendicular hits the line, using lambda
Then find the vector PM by subtracting
This dotted witht he direction vector must be 0!
USE THIS TO FIND LAMBDA, and thus coordinates ,
Now find the PM and find mod
How to find distance and coordinates of point to PLANE!
Well make up a line to find the coordinates
- this is because the direction vector of this line must be same as normal vecotr of plane, so you can now make a line equation
- use this to find the point of intersection
- now can find the distance easily by subtracting and finding the mod
How to find distance from point to plane easy
Use the equation in data sheet
How to find distance from point to 2d line.
Easily use the equation again
If they give in terms of a fair bake and say find DISTANCES! What to do and why
This is because it’s MOD
So do it sqaure and sqaure ROOT!
How ti find shortest distance between parallel lines?
Same way as point snd a line, same Formula, and method to find coordinate
(P-a) x d mod
A,l over mod d
Now disregard one of the direction vectors irrelevant !
Underlying lrocnipled for skew line distance, + how to find coordinates NEED TO KNOW
else use the FORMULA BOOK!
Basically you drawing a pepdnciual line again between the lines the shortest one , and finding distance if that
- thus yiu need a line that is bith oeorndicuakr to top line and bottom line
Write down the COordinates if the lines in terms of lambda and MEW
- thus find the vector between them PQ
- this will be perpendicualr to direction vector of top and bottom line, so dot product them to get TWO SIMULTANEOUS EQUATIONS FOR Lambda and mew
- now you have two coordinates, can find the distance between the, hella easily
