Quiz 2 Prep Flashcards
Uses for cross product
- the vector of a x b is orgothogonal to vector a and vector b. It’s not on the plane of the original vectors.
what do you need to describe a line in R^3
we need a Point(x_0,y_0,z_0) and a vector <a,b,c>. You can make another point on the vector and call it Q=((x_0)+a, (y_0)+b, (z_0)+c). Note: You can go further and scale it. Every point on this line has the form ((x_0)+at, (y_0)+bt, (z_0)+ct)`
describe a line in its parametric form.
x = x_0 + at
y = y_0 + bt
z = z_0 + ct
describe a line in its vector form.
<(x_0)+at, (y_0)+bt, (z_0)+ct>
describe a line in its symetric form.
t = (x - x_0)/a = (y - y_0)/b = (z - z_0)/z
what do you need to describe a plane in R^3
we need a Point(x_0,y_0,z_0) and a normal vector <a,b,c>. You can make another point on the vector and call it Q=((x_0)+a, (y_0)+b, (z_0)+c). Note: You can go further and scale it. Every point on this line has the form ((x_0)+at, (y_0)+bt, (z_0)+ct)
if you have to find the cross product of vectors but they are in R^2 what should you do?
make it R^3 and assume the z coord = 0
what does every point on a line have the form of?
Every point on this line has the form ((x_0)+at, (y_0)+bt, (z_0)+ct)`
how to know when they meet vs showing up to the same place at a different time.
You have your two parametric vectors. make of the vector’s parameters different from the other than set than equal to each other.
what is a normal vector?
A normal vector, also known as a perpendicular vector or orthogonal vector, is a vector that is perpendicular to a given surface at a specific point.
Equation of plane
a(x-x_0) + b(y-y_0) + c(z-z_0) = 0 or ax + by + cz = d
what if you’re trying to find where something meets or interescts and you have contridictary answers?
it doens’t meet where you want to meet.
how to find a point on a line a certain distance away from the initial point
length in question/length of vector
one thing you need to know if you want know if a line meets another line.
find parameters for both and change one of the parameters to s.
what are the normal vectors for the planes.
xy plane: <0,0,1>
yz plane: <1,0,0>
xz place: <0,1,0>
