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Let \(\mathbf{a} = \begin{pmatrix}\phantom -0\\-1\\\phantom -10\end{pmatrix}\), \(\mathbf{b} = \begin{pmatrix}2\\0\\20\end{pmatrix}\), and \(\mathbf{c} = \begin{pmatrix}4\\1\\30\end{pmatrix}\). Compute \(\mathbf{a} \times \mathbf{b} + \mathbf{b} \times \mathbf{c} + \mathbf{c} \times \mathbf{a}\)

 May 1, 2020
 #1
avatar+84 
+2

I am new to matrices so I might be wrong. 

 

Firstly we multiply a and b. For the first element (the top one on a) we multiply that by every single element in b, then we do that for the second element in a, then for the third, hence we get.

 

0+0+0=0

-1*2+0+-1*20=-22

10*2+0+10*20=220

 

Then we add all this up to give us 198.

 

Next we do the same process except for b. Thus,

 

2*4+2*1+2*30= 70

0+0+0=0

20*4+20*1+20*30=700

 

Then we add all that up to get 770. So as of right now we have 770 + 198.

 

Next we do the same process for a again but to c, hence we get

 

0+0+0=0

-1*4+-1*1+-1*30=-35

10*4+10*1+10*30=350

 

350-35=315

 

Now, we have 198+770+315, which gives us 1283.

 

I am most likely wrong :).

 May 1, 2020
 #2
avatar+20981 
0

If these are matrices, their dimensions aren't correct for multiplication.

 May 2, 2020
 #3
avatar+30086 
+3

These are vectors in 3D-space.  It looks like the question is asking about cross-products:

 

 May 2, 2020

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