## Calcmathlete Group Title 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. one year ago one year ago

1. myko Group Title

take their vector product, or prove they are multiple of each other

2. Calcmathlete Group Title

Well does a vector product of 0 allow me to conclude that they are parallel?

3. myko Group Title

yes

4. myko Group Title

g x h=|g||h|sin(theta) where theta is angle between them. It will be = 0 only if angle is 0º or 180º

5. Calcmathlete Group Title

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?

6. myko Group Title

yes

7. Calcmathlete Group Title

Oh, never mind, thank you!

8. myko Group Title

yw

9. myko Group Title

more easy: -5/3(-3i+6j-12h)=5i-10j+20k

10. myko Group Title

so -5/3g=h

11. Calcmathlete Group Title

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.

12. myko Group Title

to make -3 equal to 5

13. Calcmathlete Group Title

Oh. so you're multiplying $$\vec{g}$$ by -5/3 to make it equal $$\vec{h}$$?

14. myko Group Title

yes

15. Calcmathlete Group Title

ok, once again, thank you :)

16. myko Group Title

yw, :)