I have figured out how to determine the Dot product becasue it is fairly straight forward. However the Cross product seems to be a challenge for me as I cannot seem to grasp.

Here is the Problem

Determine: AXB if A = 3i - 2j and B = i + 2k

Need help working out this problem......

Sep 12th 2012, 12:21 PM

kalyanram

Re: Help with Calculating the Cross and Dot Product

Consider where .

Spoiler:

Now x = x = x x (why?) x + x + x + x (why?)
Now substitute their respective values and simplify.

Sep 12th 2012, 12:36 PM

Plato

Re: Help with Calculating the Cross and Dot Product

Quote:

Originally Posted by biglew404

I have figured out how to determine the Dot product becasue it is fairly straight forward. However the Cross product seems to be a challenge for me as I cannot seem to grasp.
Here is the Problem
Determine: AXB if A = 3i - 2j and B = i + 2k

Evaluate the determinate by expanding alone the first row:

Sep 12th 2012, 02:44 PM

HallsofIvy

Re: Help with Calculating the Cross and Dot Product

That is equivalent to the basic definition of x=cross product: , , .
cross product distributes over addition, and cross product is skew- symmetric ( ).

So

Because cross product is skew symmetric, , , , , , and .

That reduces the above to [tex](aq- bp)i- (ar- cp)j+ (aq- bp)k which is the same as

Sep 12th 2012, 02:45 PM

biglew404

Re: Help with Calculating the Cross and Dot Product