Help with this vector problem

[Monie3036354]

I do not understand why the normal is (1,2,2)

Edited May 8, 2014 by Monie3036354

[Rahul]

The cross product of the two vectors is AB X AC = (8, 16, 16). This cross product is the normal to the plane that AB and AC lies on, and perpendicular to both AB and AC. This normal (8, 16, 16) is parallel to the vector (1, 2, 2), and hence we can use the latter vector in place of the former when writing the equation for the plane as they are vectors in the same direction but with different magnitudes.

[Monie3036354]

How do you know it is parallel? Why can't we just use (8,8,16)? Thank you for your help

[Monie3036354]

Ohhhh! Is (1,2,2) just the simplified form?!

[Rahul]

Yes! You could use (8,8,16), but that would leave you with an extra factor of four on both sides - best just to remove it initially!

[fufufuufufufufuuu]

when do u need to factorise it? cause ive seen in some questions, if u used the unfactorised one, you wont get the answer for the upcoming question?

[MrHitNik]

not to be off topic but im kinda new around here and i want to know how i can start a new forum or discussion ar just ask a question in general.

[Rigel]

You should factorize almost always to get the equation of the plane. As a general guideline, having the smallest non-fraction terms for the normal vector is okay (you can even multiply your normal vectors by e or pi and still get the same answer, as these are linearly dependent vectors). If you use fractions I doubt they will penalize you but it gets messy when doing the dot product.

[elaifyanre]

when do u need to factorise it? cause ive seen in some questions, if u used the unfactorised one, you wont get the answer for the upcoming question?

You get the same answer--it's just that the process is more complicated.

EDIT: it's not the case if this IS the final answer, but unless they explicitly tell you to simplify it you should be fine.

Edited May 8, 2014 by ssy