Cross Product

ad - bc

the 2x2 determinant is defined as

row and col

when finding a 3x3 determinant, you can take the top elements, eliminate their (answer and answer), then find the 2d determinant of the remaining values and multiply by the respective top row value

\+,-,+

the signs of the 3 2d determinants are in order (sign, sign, sign)

area

the magnitude of the cross product of the two vectors is the () of the parallelogram bounded by the vectors

anti-commutative

(two words): the idea that if u = a x b and v = b x a, then u = -v. In another way, reversing the arguments reverses/negate/flips 180 degrees the resulting vector

Cross products have this property

0

a vector cross-product’d with itself is

non-associative

since ((a x a) x b) = 0 but (a x ( a x b)) != 0, cross product is

0

the cross product of two vectors that are linear combinations of each other is

x2*y3 -* x3y2

the i value of the cross product made from vectors x and y is

x3\**y1 - x1*\*y3

the j value of the cross product made from vectors x and y is

x1\**y2 - x2**y1

the k value of the cross product made from vectors x and y is