# Giving the equation of a line

## Homework Statement

Find the scalar equations of the line passing through p(6, 0, 3), intersecting the line (x y z) = (1 2 -3) + t(1 -2 0) and perpendicular to it

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## The Attempt at a Solution

I don't know where to start with the problem, I tried using projections and then giving out equations for the scalar product of the two lines (which is 0) and the equations of the points of intersection, but there are so many variables I can't do anything with them. I'm stuck with this problem.

Dick
Homework Helper

## Homework Statement

Find the scalar equations of the line passing through p(6, 0, 3), intersecting the line (x y z) = (1 2 -3) + t(1 -2 0) and perpendicular to it

-

## The Attempt at a Solution

I don't know where to start with the problem, I tried using projections and then giving out equations for the scalar product of the two lines (which is 0) and the equations of the points of intersection, but there are so many variables I can't do anything with them. I'm stuck with this problem.

If t0 is the value of t where they intersect then (6,0,3)-[(1,2,-3)+t0(1,-2,0)] must be perpendicular to (1,-2,0), yes? Find t0. There aren't that many variables. There's really only one.

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Got it, I can't believe i was so blind. Just asking, does the direction vector of a line always have to be given in the lowest integers as possible? (for example, we can have a direction vector (8 -4 2) and can we express it as (4 -2 1)?

Dick