Determine whether a point lies on a vector line

Question

Determine whether the given point $P(5,1,4)$ lies on the line $\vec r = (1 , 3, 4) + \lambda (2, -1, 0)$.

I don't where to start, or how to do this question.

Answer 1

your point is situated on the line since $$5=1+2\lambda$$ $$1=3-\lambda$$ $$4=4+0\lambda$$ solving this system we get $$\lambda=2$$

Answer 2

Hint:

Substitute the point $P$ in the equation: $$ \begin{pmatrix} 5\\1\\4 \end{pmatrix} = \begin{pmatrix} 1\\3\\4 \end{pmatrix} +\lambda\begin{pmatrix} 2\\-1\\0 \end{pmatrix} $$ you can say that it has the solution $\lambda=2$.