Mac 2313 - Study guides, Class notes & Summaries

The magnitude of a vector is the _______________ length of the vector/line segment The direction of a vector is the __________ direction of the arrow A negative vector is ______________ just a vector going in the opposite direction To calculate a vector: ________ point - _________ point terminal point - initial point To calculate the magnitude of a vector you use the _____________ formula distance v+w <x1 + x2, y1 + y2, z1 + z2> v-w <x1 - x2, t1 - y2, z1 - z2> cv <cx, cy, c...

Local MinD>0 AND Fₓₓ>0 Local MaxD>0 and Fₓₓ<0 Saddle PointD<0 SDT D eqD = FₓₓFᵧᵧ-Fₓᵧ² EVM1. Find val of f at critical point 2. Largest = abs max, Smallest = abs min Type-I Region1. graph between 2 funcs of x 2. g₁(x)<=y<=g₂(x) Type-II Region1. graph between 2 funcs of y

How to find the unit vector of a given vector? Vector/abs(Vector) How to find the magnitude of a given vector? sqrt(x^2 + y^2 + z^2) Is the result of a dot product a vector or scalar? scalar What is the numerical definition of a dot product? (a1b1 + a2b2 + a3b3) How to determine if two vectors are parallel? find if they are scalar multiples of each other What vector is considered to be parallel to every vector? zero vector Is the result of a cross product a vector or scalar? vector

The magnitude of a vector is the _______________ length of the vector/line segment The direction of a vector is the __________ direction of the arrow A negative vector is ______________ just a vector going in the opposite direction To calculate a vector: ________ point - _________ point terminal point - initial point To calculate the magnitude of a vector you use the _____________ formula distance v+w <x1 + x2, y1 + y2, z1 + z2> v-w <x1 - x2, t1 - y2, z1 - z2>

Local MinD>0 AND Fₓₓ>0 Local MaxD>0 and Fₓₓ<0 Saddle PointD<0 SDT D eqD = FₓₓFᵧᵧ-Fₓᵧ² EVM1. Find val of f at critical point 2. Largest = abs max, Smallest = abs min Type-I Region1. graph between 2 funcs of x 2. g₁(x)<=y<=g₂(x) Type-II Region1. graph between 2 funcs of y

How to find the unit vector of a given vector? Vector/abs(Vector) How to find the magnitude of a given vector? sqrt(x^2 + y^2 + z^2) Is the result of a dot product a vector or scalar? scalar What is the numerical definition of a dot product? (a1b1 + a2b2 + a3b3) How to determine if two vectors are parallel? find if they are scalar multiples of each other What vector is considered to be parallel to every vector? zero vector Is the result of a cross product a vector or scalar? vector

These documents contain notes on -Vectors -Coordinates in Space -3D planes in space -Vector equations and proporties

These documents contain notes on: -Lines and Planes -Position Vectors -Distance between points and lines and planes -Vector formulas and properties

These documents contain notes on: -Quadric surfaces -Graphing cylinders, paraboloids, hyperboloids, and cones -Vector equations and properties

These documents contain notes on -Cross Product -Force -Torque -Area