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Given \(\vec{g} = -3\vec{i} + 6\vec{j} - 12\vec{k}\) and \(\vec{h} = 5\vec{i} - 10\vec{j} + 20\vec{k}\), how could I prove that \(\vec{g}\) and \(\vec{h}\) are parallel? Please explain the reasoning.

Mathematics
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take their vector product, or prove they are multiple of each other
Well does a vector product of 0 allow me to conclude that they are parallel?
yes

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Other answers:

g x h=|g||h|sin(theta) where theta is angle between them. It will be = 0 only if angle is 0º or 180º
Ok, just clarifying, is it because using the formal definition of the magnitude of a vector product, if \(\theta\) = 0º or 180º, it would cause the entire thing to become 0, and therefore parallel since an angle of 0º or 180º would be the same line or parallel?
yes
Oh, never mind, thank you!
yw
more easy: -5/3(-3i+6j-12h)=5i-10j+20k
so -5/3g=h
Ok. that is the reason the book gave me, so I'm curious as to why that works...I don't see where -5/3 comes from.
to make -3 equal to 5
Oh. so you're multiplying \(\vec{g}\) by -5/3 to make it equal \(\vec{h}\)?
yes
ok, once again, thank you :)
yw, :)

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