Vectors Forgot Flashcards
If perpendicular two vectors what is dot product v
To 0, a dot b is 0
Vector equation
Remmeber any two vectors PERPENDICULAR are 0 dot
So r-a dot n must be 0
Expand, - a .n = to d
How to find angle between two planes
Find the angle between normals
But remember to do 180- if you want the acute angle?
How to see Follower for vector 3d
Find equation
Equate to new point
Then see if lambda consistent , if they are then it id
He ti change the vector equations
Can simply the grsdient direction vector
Csn subtrsvt ir add this to the position vecotr
How to convert between Cartesian vector
For to Cartesian x - Positionen/ direction = y - position etc
Vector to Cartesian
= - thingd become position, denominator direction
Can multiply by -1 if needed
For one zero vs 2 zeroes?
If one zero, then that value is always its value,
If itstwo zero we don’t , need the third variable to describe the line , we know y is whatever
So just say x = y =
The intersection of two 3d lines, what 3 scenarios can they be
First chekc if parallel, so if direction vectors multiples of Esch other , in which case don’t intersect
Now equate and solve for lambda mew, if these return consistent points, then intersect, if not then they are skew and never meet
Now if yiu sub in to third equation and not consistent thst tells you straight away skew, but if consistent then they intersect
If yiu get obtuse angle for the angle between two p
Snes , how to find scute
180-answer
Intersection kine and plane
Equate general point xyz, find parameters, out itnonplane , solve for lambda put back get coordinate
To check out back itnonllane should equal that’s it suspoosed to
Angle between line and plane?
The angle between the normal and direction vector of the plane will die the rgive yiu sn kbtuse or active angle
Get the acute angle by 180-x
Now MUST DO 90-X to get the angle as shown
