# Essential Formulas - Flashcards

## Flashcard Deck Information

 Class: MATH 32A - Calculus of Several Variables Subject: Mathematics University: University of California - Los Angeles Term: Spring 2011
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Mode:         ? pages *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
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 *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
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 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
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 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
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 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 = |a||b| 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|
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 *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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## List View: Terms & Definitions

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*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 originx^2 + y^2 + z^2 = r^2
*drag IMG to new window for full view*Vector between 2 points A and B
unit vectora 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 aThe result will become 0.
Special property(s) of resulting vector from cross product aXbIt'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 = |a||b|
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