Finding Vectors in cartesian form

Question

I am stuck on this question could you please help me.

Find,in Cartesian form, the equations of the straight line through the point with position vector (-1,2,-3) parallel to the direction given by (2,1,-2)

Any help is appreciated. Thanks

Answer 1

$$x=-1+2t\\y=2+t\\z=-3-2t$$ or simply $$(x,y,z)=(-1,2,-3)+t(2,1,-2)$$

Answer 2

A line $L$ is uniquely specified by giving any point $P_0=(x_0,y_0,z_0)$ on $L$ and any vector $u=(a,b,c)$ parallel to $L$ as follows: $$\frac{x-x_0}{a}=\frac{y-y_0}{b}=\frac{y-y_0}{c}$$