Lines and Planes in space Question

[Guest]

Hi everyone, i have a midterm exam coming up and i'm looking at problems in the section of the book to help myself prepare. Can anyone answer this question for me? I have attempted to answer this problem but without the answer i don't know if i'm right.

It is problem # 114 in CALCULUS 8th edition by larson, hostetler and edwards, secction 11.5 page 809. It will be in section 10.5 in the 7th edition.

Show that the plane 2x-y-3z=4 is parallel to the line
x= -2+2t
y= -1+4t
z= 4

and find the distance between them.

I tried using the techniques given in the book but it's not for a plane and line.

I drew the plane and line on a calculator and tried to count the boxes, but i cannot. i honestly wouldn't know where to begin to do this mathematically.

Can someone do this one out for me? It's not a homework, i just need to see it done out step by step so i can follow it, along with the answer.

Thank you guys! Really desperate...

 

[galactus]

To determine whether a plane is parallel to the line, look at the direction vector. Remember, from my response to your other post?.

The direction vector is the 'coefficients' of t in the parametric equations.

The vector, v=[2,4,0]

The vector, n=[2,-1,-3] (the coefficients of the plane equation).

In order for them to be parallel, the vectors v and n must be perpendicular.

Take the dot product. Is it equal to 0?. If it is, then the vectors are perpendicular. Ergo, they are parallel.

Then, use the formula from the other post to find the distance between them.