Question

Give a vector parametrization for the line that passes through P(-1,2,-3) and is parallel to the line 2(x+1)=4(y-3)=z.

I know that r(t)=r0 + td.

So r0=-i+2j-3k

But I'm not sure how to get the values for (d1, d2, d3).

Answer 1

You just need to find two points on the line.

Try \(x=0\) then solve for \(y\) and \(z\).

Answer 2

then try \(x=1\) and solve for \(y\) and \(z\).

Answer 3

Ok, for the first one I find:

x=0, y=3.5, z=2

For the second,

x=1, y=4, z=4

Am I supposed to subtract these two points to find d(1, 0.5, 2)?

If so, then that's the wrong answer. The correct d is d(2,1,4).

Answer 4

Hahahahahahaha.

Answer 5

The slope of a line can't be \(\frac 42\) if my book says it is \(2\)!

Answer 6

Oh. Lol.

Answer 7

The magnitude of the direction vector does not matter in this case.

Answer 8

Ok cool. Hahaha. I have had a rough week. My Calc III prof is russian.

Answer 9

Anyhow, thanks a bunch. I have learned much from you.

Answer 10

Good luck.

Answer 11

Thanks, haha.