Use LEFT and RIGHT arrow keys to navigate between flashcards;
Use UP and DOWN arrow keys to flip the card;
H to show hint;
A reads text to speech;
14 Cards in this Set
- Front
- Back
|
Dot product |
A1B1 + A2B2 + A3B3 scalar |
|
|
Cross Product |
Matrix, remember the second factor switch |
|
|
Scalar Projection |
Compab = a.b/|a| b onto a |
|
|
Vector projection |
Projab = (a.b/|a|²)a B onto a |
|
|
Vector angles |
Cos(O) = a.b/|a||b| |
|
|
Orthogonal |
If and only if the dot product = zero |
|
|
Finding the equation of a plane method 1 - point and vector |
Point (p1, p2, p3) and vector <a, b, c> Equation is a(x-p1) + b(y-p2) + c(z-p3) = 0 |
|
|
Plane equations method 2 - 3 points |
Create two vectors - take their cross product - use that with any point and do method 1. |
|
|
Planes equations method 3 - point and parametric equation |
Pick any two points for t - receive two points - do method 2 |
|
|
Distance between planes |
Find a point on the plane (set y and z to zero) point (p1,p2,p3) Plane ax + by + cz + d = 0 D = |ap1 + bp2 + cp3 + d|/sqrt(a² +b² + c²) |
|
|
Unit Tangent vector |
T = r'(t) / |r'(t)| |
|
|
Arc length |
Integral of sqrt( (x'² + y'² + z'²)) |
|
|
Limit does not exist |
Set y to zero - get value Set x to zero - get value If values don't equal - limit dne |
|
|
Partial derivatives |
Derivative for y, x is a constant Derivative for x, y is a constant |
