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27 Cards in this Set
- Front
- Back
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vector, parametric, symmetric |
r = <a,b,c> + t<x,y,z> x(t)=a+xt t = x(t)-a/x |
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vector orthogonal to two other vectors |
v = (uxw)/|uxw| |
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distance from point to the line |
let t=0 & 1 then d = |QR x QP|/|QR| |
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scalar projection |
comp a B = (a • b)/|a| |
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vector projection |
proj a B = (a • b)/|a|^2 * a |
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measure of three angles given three vertices D E & F |
a = DE, b = DF then angle of D = arccos (a • b)/|a||b| |
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find volume of parallelopiped with 4 adjacent vertices |
V = a • (b x c) so PQ • (PR x PS) |
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if v x w = <3,1,4> and v • w = 2, what's angle between them |
tan € = |v x w|/(v • w) |
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find two unit vectors orthogonal to vectors a & b |
a x b = ortho v--- unit vector is v/|v| |
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Paraboloid |
z = (x/a)^2 + (y/b)^2 |
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Ellipsoid |
(x/a)^2 + (y/b)^2 + (z/c)^2 = 1 |
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Hyperbolic Paraboloid |
z = (x/a)^2 - (y/b)^2 |
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Hyperboloid One Sheet |
(x/a)^2 + (y/b)^2 = (z/c)^2 + 1 |
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Hyperboloid Two Sheets |
(x/a)^2 + (y/b)^2 = (z/c)^2 - 1 |
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Elliptic Cone |
(x/a)^2 + (y/b)^2 = (z/c)^2 |
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Intersection of line and plane |
plug in line to plane and solve for t |
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find equation of plane through point P and perpendicular to vector n |
plane has slopes of vector and is equal to when the point is plugged into the plane |
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Three vertices P Q & R Find Area of PQR |
PQ • PR = |PQ||PR|cos£ then Area = 1/2 |PQ||PR|sin£ |
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Three vertices P Q & R Find equation of plane contain P Q & R |
PQ x PR which is the slopes of the plane and then plugin P |
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two planes are parallel if |
there is some k value to make the equations equal |
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two planes are perpendicular if |
dot product of the two is equal to 0 |
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distance from point to a plane |
D = |ax + by + cz + d|/sqrt(a^2 + b^2 + c^2) |
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directional cosines of the vector v = ai + bj + ck |
cos £ = a/|v| cos ¢ = b/|v| cos € = c/|v| |
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work equation |
w = |F||AB|cos £ |
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v and u are orthogonal if |
v • u = 0 |
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v and u are parallel if |
v x u = 0 |
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torque equation |
|T| = |r||F|sin £ |
