Question

Which of the following is not a direction vector for the plane 3x-2y-z+4=0?

a) (3,-2,-1)
b) (0,-2,4)
c) (2,2,2)
(2,4,-2)

How do you know when its not a direction vector?

Answer 1

@Vocaloid

Answer 2

disclaimer: had to look this one up but

I believe you would plug in the x,y, and z value for each coordinate

the +4 can be neglected [not entirely sure why, I think it has something to do with the fact that we are only considering direction]

3x-2y-z = 0

then just see which answer choice makes this statement true

Answer 3

idk when they'll be on but @hero @Angle

Answer 4

oh wait, it says which one is ~not~ a direction vector so you would pick the vector that makes the statement false

Answer 5

Yeah, so I got this:
(3,-2,-1)
So option A is off.

Answer 6

So let me try plugging in now

Answer 7

So hold up. B and C make the statement false. :|

Answer 8

hm?

3x-2y-z = 0

B gives

(0,-2,4) --> 3(0) - 2(-2) - 4 = 0

C gives

(2,2,2) --> 3(2) - 2(2) - 2 = 0

so I believe C and B are both still direction vectors

going back to choice A I end up with

3(3) - 2(-2) - 1(-1) which is 9 + 4 + 1 = 14 so I'm actually inclined to go w/ choice a

Answer 9

Okay, but if we do option d the statement is also not correct. It gives us 4=0. So?

Answer 10

And I'm pretty sure option A can't be correct.

Answer 11

hm. I can ask somebody else's opinion b/c I'm still not entirely sure how to do this

Answer 12

Okay, please do. Tysm!

Answer 13

@liam alright I just got back

for a direction vector, you consider every plane that is parallel to the original plane, not just the original plane, so the +4, for the sake of calculations, can be disregarded

so instead of calculating 3x-2y-z+4=0 you can simply use 3x - 2y - z = 0 and plug in the coordinates of each vector