Hi, just wanted to double check this question off with you people.

Find a vector equation through the point (0, 14, -10) and parallel to the line x= -1 + 2t, y= 6-3t, z=3+9t

r = r0 + tv

r0 = 0i + 14j - 10k

the vector we need can be derived from the line x= -1 + 2t, y= 6-3t, z=3+9t

it is <2, -3, 9> [i was unsure at this part, am I correct here?]

so r0 + tv = (2t)i + (14-3t)j + (9t-10)k

hence vector equation = (2t)i + (14-3t)j + (9t-10)k

parametric equation = x =2t, y=14-3t, z=9t-10

another question i wanted to ask is why is it helpful to know how to find the parametric equation? How does it make life more convenient, or how is it useful?

also anyone have resources on where I can learn more with lines and planes. I feel my conceptual skills could use some tightening up.

furthermore, do any programs exist that would allow me to plot planes and lines in 3-d spaces? I tried wolfram but either it can't do it (tried plotting x=1, y=0, z=0) or i just don't know how to use it.

Thanks!