Parametric Eqn of line thru (0,1,2) perp to x=1+t,y=1-t,z=2t

[acpodgorski]

The problem tells me to:

Find the parametric equations for the line through the point (0,1,2) that is perpendicular to the line x=1+t,y=1-t,z=2t and intersects this line.

i know that the equation for the line starts with the point plugged in for a,b,c in x=a+_t, y=b+_t, z=c+_t but what do i need to get from the other line's equation to complete this?

 

[pka]

The problem tells me to Find the parametric equations for the line through the point (0,1,2) that is perpendicular to the line x=1+t,y=1-t,z=2t and intersects this line. i know that the equation for the line starts with the point plugged in for a,b,c in x=a+_t, y=b+_t, z=c+_t but what do i need to get from the other line's equation to complete this?

Pick two points on the on the given line: say (1,1,2) & (0,2,-2).
Use the given point with these points to determine two vectors: <1,0,0> & <0,1,-4>
Find the cross product <1,0,0>X<0,1,-4>=<0,4,1>.
Using the direction vector of the line <1,-1,2>, find <0,4,1>X<1,-1,2>.
That is the direction vector of the line you need.

 

[maeveoneill]

Re:

Pick two points on the on the given line: say (1,1,2) & (0,2,-2).
Use the given point with these points to determine two vectors: <1,0,0> & <0,1,-4>
Find the cross product <1,0,0>X<0,1,-4>=<0,4,1>.
Using the direction vector of the line <1,-1,2>, find <0,4,1>X<1,-1,2>.
That is the direction vector of the line you need.

Why do you need to pick two points on the line.. can you just not just pick one and also use the given point.. and use the vector <1,-1,2>?

 

[pka]

Re: Re:

Why do you need to pick two points on the line.. can you just not just pick one and also use the given point.. and use the vector <1,-1,2>?

Well, try that why don’t you.
Remember that the line you are writing must be perpendicular to the give line.