Vectors Flashcards
Intersection of two lines
Rewrite as x + yλ, and a + bμ form
Set equal to each other
Solve simultaneous using two of them
Plug in to third to check
Intersection of line and plane
Write line equation as x + yλ
Sub in as a point on plane
Solve lambda
Plug answer in for point
Angle between two lines
Cosθ = a.b/(|a| x |b|)
A and b are direction vectors of lines
Angle between line and plane
Same as two lines
Use normal of plane and direction vector
Angle between two planes
Same as two lines
Use the normals for planes
Shortest distance between point and line
Find vector between point and point on line
Find modulus of that
Find cosθ dotting direction vector and vector worked out
Work out sinθ from this (use pythag for unknown)
Multiply sinθ by modulus worked out
Shortest distance between two lines
If parallel, use same method as point and line
Shortest distance between point and plane
Formula sheet
Shortest distance between two skew lines
Cross product two direction vectors to find the perpendicular vector (q)
Find vector between two given point vectors (p)
Shortest distance is |(p.q)/(|q|)|
How do you know two lines are perpendicular?
Dot product equals zero
