Question

How do you determine the direction for the normal: (3,2,4)

Answer 1

Direction vector*

Answer 2

What do you mean?

Answer 3

Sorry. I didn't phrase my question right. I know how to find the direction vector of a line from the normal vector of the line when in 2 space since they are perpendicular to each other. For ex. The normal may be (2,1) so I could assume the director vector if line would be (-1,2) or (1,-2) but would I do so, if it's in 3 space

Answer 4

Of the line*

Answer 5

In 3D, there are infinity many vectors that are perpendicular to a given line. Of you can just imagine the vector rotating around the line.

There is a test whether two vectors in 3D are perpendicular, and that is called the dot product.

two vectors are perpendicular if the dot product between them equals 0

Answer 6

suppose vector (a,b,c).

(a,b,c) dot (3,2,4) = 0
2a + 3b + 4c = 0

so all vectors (a,b,c) that satisfy the equation above are perpendicular to (4,2,4)

Answer 7

*(3,2,4)*

Answer 8

So , -2, -3, and -4 could possibly be the direction vector of the line?

Answer 9

the equation was supposed to be
3a + 2b + 4c = 0

so if (a,b,c) = (-2,-3,-4), then
3(-2) + 2(-3) + 4(-4) = -28, which is not 0. Thus (-2,-3,-4) is not perpendicular to (3,2,4)

Answer 10

Thanks!