Chapter 6 Formuls Flashcards
Skew lines
Lines that are in different planes, are not parallel and do not intersect
Standard vector form with parameter t
<x,y,z> = (Xo,Yo,+Zo) + t <a,b,c>
Parametric form
x =Xo+ta
y= Yo +tb
z=Zo +tc
Symmetric form
X-Xo/a=Y-Yo/b=Z-Zo/c
Distance between skew lines
Usually refers to the shortest distance, the shortest distance is equal to the length of the perpendicular line between them
Cross product of vectors
results in vector perpendicular to both lines
Cross product fromula
d = (p1-p2) x (v1xv2)/ mag(v1Xv2)
x = cross product not times
Finding the cross product
<a1,a2,a3><b1,b2,b3>
<a2b3-a3b2/a3b1-a1,b3/a1b2-a2,b1>
Testing for skewness
1). check slopes
2). check if intersecting
Parallel lines
Same slope
Perpendicular lines
Meeting angle must be 90
product of slope = -1
Neg reciprocal always the other slope
Coplanar lines
lie on the same plane
non-coplanar
lines that don’t lie on the same plane
Tetrahedron
A Platonic solid made from triangles and has 3 sides meeting at every corner (Pyramid)
Hexahedron
A Platonic solid made from squares and has 3 sides meeting at each corner (cube)
Octahedron
A Platonic solid where sides consist of triangles and that has 4 triangle sides meeting at every corner (two pyramids with bases to each other)
Dodecahedron
A Platonic solid that has pentagons for its sides and has 3 pentagon sides meeting at every corner (12 sided dice)
Isosahedron
A platonic solid with triangles for sides and that has 5 triangle sides meeting at every corner (alphabet dice)
Cone formulas
SA base = PixR^2
SA curved side = pi x r s
s = sqrt(r^2+h^2)
comp Sa = pi r^2 + pi x r x s
h and r only = pi r^2 + pi x r sqrt(r^2+h^2)
volume = (pi r^2 x h) / 3
Pyramids
SA = B + (PxS) / 2
V = (BxH) / 3
Sphere
V = (4/3) x pi x r^3
SA = 4 x pi x r^2
Cylinder
SA = 2piR x (r+h)
V = piR^2 x h
Prisms
SA = 2B+Ph
V = BxH
P= perimeter of base
cube
V = S^3
V of rectangular prism = L x W x H
