- Colloquium
- “Suspect Something Fishy? How Statistics Can Help Detect It, Quickly!”
- Dr. Aleksey Polunchenko, SUNY Binghamton
- Wednesday, Sept. 23, 2:45
- Newton 204
- Extra credit for short write-ups, like last colloquium; email fine
- Airplane from problem set 2
- Section 12.5, 2nd Half
- Planes characterized by normals (perpendicular vectors to point(s) in plane)
- Plane equation: Ax + By + Cz = D
- A, B, C, D constants
- Normal = ⟨A,B,C⟩
- (Acute) angle between planes = angle between normals
- Distance formula from point to plane
- Examples
- Equation(s) for plane with normal ⟨1,1,1⟩ and containing
point (2,0,1)
- A(x-x0) + B(y-y0) + C(z-z0) = 0
- Normal = ⟨A,B,C⟩ = ⟨1,1,1⟩
- (x-x0) + (y-y0) + (z-z0) = 0
- x0, y0, z0 are coordinates of some point in plane
- x - 2 + y + z - 1 = 0
- x + y + z = 3
- Equation(s) for plane containing points (2,0,0), (0,1,1) and
(1,0,2)
- How can you use dot product to test if point (p,q,r) lies in
plane Ax + By + Cz = D?
- Where does line ⟨ -1+t, -1+2t, t ⟩ intersect plane 2x + y - z = 5?
- Plug parametric expressions for x, y, z into equation of plane and solve for t
- This idea generalizes to intersections between lines and other implicit surfaces, e.g., all quadrics
- Line along which 2x + y - z = 5 and x - 3y + z = 1 intersect?
- N1 × N2 = ⟨-2,-3,-7⟩ = V
- (2,0,-1) is on both planes = P
- So the line is P + tV = (2,0,-1) + t⟨-2,-3,-7⟩
- Equation(s) for plane with normal ⟨1,1,1⟩ and containing
point (2,0,1)
- Vector-valued functions and their derivatives
- Read section 13.1