To look at something that is somewhat related to the type of result you need for this problem, examine what a straight line looks like in 3 dimensions: You will typically see something like ##\frac{x-5}{3}=\frac{y-2}{5}=\frac{z-6}{4}=t ## and this line passes through ## (5,2,6 ) ## and it is in the direction of the vector ## \vec{v}=3 \hat{i}+5 \hat{j}+ 4 \hat{k} ##. You can even normalize this vector ## \hat{v} ## to a unit vector in that direction. ## \\ ## Basically the equation of this line is the parameterization ## x=3t+5 ##, ## y=5t+2 ##, and ## z=4t+6 ##. It might appear clumsy, but we can't do a simple line in 3 dimensions like we do a line in two dimensions. e.g. the equation ## 3x+5y +2z+4=0 ## represents a plane, rather than a line.