1. ## Find parallel Vector

Can somebody help with this. I am finding it confusing. Not too good with this vector stuff.

Determine if the plane given by -x+2z=10 and the line given by vector r=<5,2-t,10+4t> are orthogonal, parallel or neither.

In particular, how do I find a line parallel to vector r?

2. A line is perpendicular to a plane if its direction is parallel to the normal.
A line is parallel to a plane if its direction is perpendicular to the normal.

So work with $\displaystyle D=<0,-1,4>~\&~N=<-1,0,2>$.
Are they perpendicular or parallel?

3. How did you derive D?

4. Originally Posted by p75213
How did you derive D?
If the line $\displaystyle r(t)=<a+ut,b+vt,c+wt>$ then its direction vector is $\displaystyle D=<u,v,w>$.

5. Originally Posted by p75213
Can somebody help with this. I am finding it confusing. Not too good with this vector stuff.

Determine if the plane given by -x+2z=10 and the line given by vector r=<5,2-t,10+4t> are orthogonal, parallel or neither.

In particular, how do I find a line parallel to vector r?

If Ax+By+Cz+D=0 is some plane, the perpendicular victor to this plane is the vector (A,B,C), in your case (0,-1,4)

r=<5,2-t,10+4t> is a line, with vector direction (0,-1,4).

If the dot product of above two vectors is equals to zero then the line and the plane are orthogonal.

If two vectors have linear dependency then they are parallel.