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Karma
Class:  MATH 32A  Calculus of Several Variables 
Subject:  Mathematics 
University:  University of California  Los Angeles 
Term:  Spring 2011 
*drag IMG to new window for full view*  Scalar projection of B onto A 
*drag IMG to new window for full view*  Vector projection of B onto A 
*drag IMG to new window for full view*  Distance between 2 points 
*drag IMG to new window for full view*  Angle between the vectors 
*drag IMG to new window for full view*  Magnitude (length) of a vector 
Equation of a sphere  (x  h)^2 + (y  j)^2 + (z  k)^2 = r^2 
Equation of a sphere centered at the origin  x^2 + y^2 + z^2 = r^2 
*drag IMG to new window for full view*  Vector between 2 points A and B 
unit vector  a vector whose length is 1 
*drag IMG to new window for full view*  Finding the unit vector of vector V 
Formula(s) for calculating work  F D cosӨ OR F • D 
*drag IMG to new window for full view*  Cross Product setup 
Cross product of a X a  The result will become 0. 
Special property(s) of resulting vector from cross product aXb  It's orthogonal to both vectors 'a' and 'b' 
How to check for orthogonality to 'a' or 'b' of a cross product?  [ (a X b) • a ] OR [ (a X b) • b ] 
Finding angle between 'a' and 'b' with a cross product  (a X b) = a b sinӨ 
How can the cross product prove that 2 nonzero vectors are parallel?  a X b = 0 
How to use the dot product to prove orthogonality?  a • b = 0 
How can you prove that 2 nonzero vectors are parallel with the dot product?  a • b = ab 
Is it possible to find the area of a parallelogram given vectors 'a' and 'b'? If so, how?  Yes. Find the area by taking the magnitude of the cross product. a X b 
*drag IMG to new window for full view*  Volume of a parallelpiped 
How does the scalar triple product prove that points a, b, and c are coplanar?  The scalar triple product must equal 0. a • (b X c) = 0 
Formula(s) for calculating Torque   r X F = r F sinӨ ==> Where r is the length of the tool (i.e.wrench) and F is the amount of force (usually in Newtons) applied 
Front 
Back 


*drag IMG to new window for full view*  Scalar projection of B onto A  
*drag IMG to new window for full view*  Vector projection of B onto A  
*drag IMG to new window for full view*  Distance between 2 points  
*drag IMG to new window for full view*  Angle between the vectors  
*drag IMG to new window for full view*  Magnitude (length) of a vector  
Equation of a sphere  (x  h)^2 + (y  j)^2 + (z  k)^2 = r^2  
Equation of a sphere centered at the origin  x^2 + y^2 + z^2 = r^2  
*drag IMG to new window for full view*  Vector between 2 points A and B  
unit vector  a vector whose length is 1  
*drag IMG to new window for full view*  Finding the unit vector of vector V  
Formula(s) for calculating work  F D cosӨ OR F • D  
*drag IMG to new window for full view*  Cross Product setup  
Cross product of a X a  The result will become 0.  
Special property(s) of resulting vector from cross product aXb  It's orthogonal to both vectors 'a' and 'b'  
How to check for orthogonality to 'a' or 'b' of a cross product?  [ (a X b) • a ] OR [ (a X b) • b ]  
Finding angle between 'a' and 'b' with a cross product  (a X b) = a b sinӨ  
How can the cross product prove that 2 nonzero vectors are parallel?  a X b = 0  
How to use the dot product to prove orthogonality?  a • b = 0  
How can you prove that 2 nonzero vectors are parallel with the dot product?  a • b = ab  
Is it possible to find the area of a parallelogram given vectors 'a' and 'b'? If so, how?  Yes. Find the area by taking the magnitude of the cross product. a X b  
*drag IMG to new window for full view*  Volume of a parallelpiped  
How does the scalar triple product prove that points a, b, and c are coplanar?  The scalar triple product must equal 0. a • (b X c) = 0  
Formula(s) for calculating Torque   r X F = r F sinӨ ==> Where r is the length of the tool (i.e.wrench) and F is the amount of force (usually in Newtons) applied 
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