Proving that this vector eqn is correct...

[ttpp1124]

Homework Statement

I solved it, but can someone lmk if there's a way to see if I'm correct..? Thank you in advance!

Relevant Equations

n/a

 

[Charles Link]

I agree with your solution.

 

[ttpp1124]

I agree with your solution.

Thank you

 

[archaic]

So that you do it quicker next time, remember that the directional vector of a vector $\vec u$ perpendicular to a vector $\vec v = (a,\,b)$ is always$(-b,\,a)$. Knowing that, you can directly say that the directional vector of $\vec q$ is $(-2,\,-3)=-(2,\,3)$, thus $\vec q=(c,\,d)-s(2,\,3)$.
Yes it is negative the one you found, but consider both cases when $s$ is positive and when it is negative; we'll reach the same points.