1. Vectors

I need help with the following 2 questions please

1. Prove that the line x=1+2t, y=-1+3t, z=2+4t is parallel to the plane x-2y+z=6.

2. Find the distance between the line and the plane in 1.

thanks

2. If D is the direction vector of the line and N is the normal vector of the plane then if $D \cdot N = 0$ then the two are prallel.

3. Originally Posted by smiler
I need help with the following 2 questions please

1. Prove that the line x=1+2t, y=-1+3t, z=2+4t is parallel to the plane x-2y+z=6.

2. Find the distance between the line and the plane in 1.

thanks
the line is parallel to the vector $v=<2,3,4>$ and the plane is perpendicular to the vector $r=<1,-2,1>$

like what plato said, try to check of the vectors v, r are perpendicular to each other, i.e their dot product is 0, then the line and the plane are parallel..