Equation for a line through an origin

[Poetria]

Homework Statement

Find the equation for the line through the origin that is perpendicular to the vector (-1,4). Enter the equation in the form: $a*y+b*x=0$

Relevant Equations

Dot product of the vector (-1,4) and the vector parallel to the line has to be 0.

Why is this wrong?
$$-4*y+x=0$$

$$\vec (-1, 4)\cdot\vec (4,1)=0$$

 

[fresh_42]

Why do you think it is wrong?

 

[Poetria]

It has been marked as wrong by an automatic grader. But I don't understand why. :(

 

[fresh_42]

It has been marked as wrong by an automatic grader. But I don't understand why. :(

There is no unique solution to $ay+bx=0$ because all $acy+acx=0 \;(c\neq 0)$ are solutions, too. Could be that whatever checked it expected a normalized vector, or a positive $a$.

 

[Poetria]

It is stated: expression in the form $a*y+b*x$. I will try with the positive a then.

$$4*y-x=0$$

Many thanks. :)