VECTORS :((((((((( Flashcards
What is the equation of a line in vector form?
r = a + lambda b
What is the equation of a line in cartesian form?
(x-a)/b = (x-c)/d = (z-e)/f
What is the angle between two lines?
cos theta = a.b / (mod(a))(mod(b))
When are vectors perpendicular?
If a.b = 0
What is the vector form of a plane?
r = a + lambda b + mu c
What is the cartesian form of a plane, unsimplified?
n1x + n2y + n3z = d; d = a.n
What is the simplified cartesian form of a plane?
r.n = a.n so r.n = d. r is a general point. To get back to other form, replace r with (xyz) stack.
What is the angle between a line and a plane? r = a + lambda b; r.n = k
sin theta = b.n/(mod(b))(mod(n))
What is the angle between two planes?
r.x = k1; r.y = k2
cos theta = (x.y)/(mod(x))(mod(y))
How do you determine if lines are skew or not?
Write and equate both line equations, solve simultaneously- if consistent they aren’t skew
How do you find the intersection of a line and a plane?
Write plane in r.n = k, then replace general point r with vector equation of the line.
What is n in the plane equation?
Normal vector to the plane
How do you find the shortest distance between two parallel lines?
Find when AB is perpendicular to both lines.
How do you find the reflection of a point in a plane?
Find line normal to plane that passes through P. Find intersection. Find distance. Then make it twice as far as that.
