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1. See attached image please!
2. For part (a), I applied the cross product and got (6i  2k) for ([itex]\vec{A}[/itex]x[itex]\vec{B}[/itex]. I got (6i + 2k) for ([itex]\vec{B}[/itex] x [itex]\vec{A}[/itex]).
For part (b), [itex]\vec{C}[/itex] was simply (6i  2k)  (6i + 2k) = (12i 4k).
For part (c), the magnitude of [itex]\vec{C}[/itex] was simply 12.65 and for the magnitude of two times ([itex]\vec{A}[/itex] x [itex]\vec{B}[/itex]) is 12.65. So they are equal. But WHY? I can prove it mathematically, but I'm having some trouble with this.
I do think that it is because ([itex]\vec{A}[/itex]x[itex]\vec{B}[/itex] is equal in magnitude but opposite in direction to ([itex]\vec{B}[/itex] x [itex]\vec{A}[/itex]), therefore, the magnitude for 2 times ([itex]\vec{A}[/itex] x [itex]\vec{B}[/itex]) ought to equal the magnitude of ([itex]\vec{C}[/itex])
2. For part (a), I applied the cross product and got (6i  2k) for ([itex]\vec{A}[/itex]x[itex]\vec{B}[/itex]. I got (6i + 2k) for ([itex]\vec{B}[/itex] x [itex]\vec{A}[/itex]).
For part (b), [itex]\vec{C}[/itex] was simply (6i  2k)  (6i + 2k) = (12i 4k).
For part (c), the magnitude of [itex]\vec{C}[/itex] was simply 12.65 and for the magnitude of two times ([itex]\vec{A}[/itex] x [itex]\vec{B}[/itex]) is 12.65. So they are equal. But WHY? I can prove it mathematically, but I'm having some trouble with this.
I do think that it is because ([itex]\vec{A}[/itex]x[itex]\vec{B}[/itex] is equal in magnitude but opposite in direction to ([itex]\vec{B}[/itex] x [itex]\vec{A}[/itex]), therefore, the magnitude for 2 times ([itex]\vec{A}[/itex] x [itex]\vec{B}[/itex]) ought to equal the magnitude of ([itex]\vec{C}[/itex])
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