Thursday

October 2, 2014

October 2, 2014

Posted by **matt** on Wednesday, September 14, 2011 at 12:53pm.

- calculus -
**Steve**, Thursday, September 22, 2011 at 10:27amIf you look for some list of identities for vector products, such as wolfram: cross product you will find the following:

A.(BxC) = det(ABC)

(AxB)x(CxD) = det(ABD)C - det(ABC)D

If we adapt this formula to our problem, we need to set

A = b

B = c

C = c

D = a

Now, we plug and chug:

bxc x cxa = det(bca)c - det(bcc)a

Now, a determinant is zero if two rows are the same. So, we can toss out he last term on the right, and we are left with just

bxc x cxa = det(bca)c

AxB.C = C.AxB so,

axb . det(bca)c = det(bca)c . axb

= det(bca) * det(cab)

When we swap columns, the detrminant changes sign. Swapping columns twice, we get

det(bca) * det(cab) = det(abc) * det(abc) = (a.bxc)^2

**Answer this Question**

**Related Questions**

calculus - Find two unit vectors that make an angle of 60° with v = ‹3, 4›. Give...

Chemistry - When drawing the 'dot and cross' diagram to show the ionic bonding ...

Math - There are four people that want to cross a bridge. Sam can cross in 1 ...

Math: Cross Product - Prove that | a x b | = (sqrt) [(a (dot) b)(b (dot) b) - (a...

maths magic - There are A,B,C,D at one end of the bridge.they have to cross ...

Chemistry - Hi Dr Bob, I understand the 2nd method but need to clarify the 1st ...

MATH - FOUR CYCLISTS A,B,C&D WANTS TO CROSS A BRIDGE BUT DUE TO BAD CONDITION OF...

BIOLOGY - A girl crossed a pure short, black haired animal with a pure long, ...

Genetics/Di hybrid Cross - Can someone show me how to set up this dihybrid cross...

math - i am very confused with the question: when a cross tile is placed on a ...