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 \(\mathbf{a} \times \mathbf{b} + \mathbf{b} \times \mathbf{c} + \mathbf{c} \times \mathbf{a}\)
+84 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 :).
