# Thread: Equations of these lines and planes

1. ## Equations of these lines and planes

Hi.
For lines, i know primarily we need a point, and a vector parallel to the line.

But for this question,
Find the equation of the line through (2,1,0) and perpendicular to both i+j and j+k.

How do i derive the parallel vector. What doe sit mean if the line is perpendicular to i+j and j+k ? How do I use this.

Thanks

2. ## Re: Equations of these lines and planes

It looks lie this problem expects you to know that the cross product of two vectors is perpendicular to both.

Once you have the vector, <A, B, C>, the line parallel to that vector, through point (a, b, c) is given by x= Ax+ a, y= Bx+ b. z= Cx+ c.

3. ## Re: Equations of these lines and planes

Oh i think I get it.

Is i+j ahd j+k simply another way to say (1,1,0) and (0,1,1) ?

4. ## Re: Equations of these lines and planes

I would have put it the other way around- (1, 1, 0) and (0, 1, 1) are (somewhat ambiguous- it can be confused with a point) ways of writing what should be called i+ j and j+ k.