Question

find the equation of the line drawn through the point (1,0,2) to meet at right angles the line (x+1)/3 =(y-2)/-2 = (z+1)/-1

Answer 1

let A = (-1,2,-1) , which is a point on the line that we can glean from the equation you provide ([sets everything to zero]

let B = (1,0,2), the first point you mention in your question, from which the new line is to be drawn

let X = the point on the line you want to find

now, the line equation you give can also be written as (x,y,z) = (-1,2,-1) + t (3, -2, -1), with t as the parameter, right?

furthermore, XA • XB = 0 where XA and XB are the direction vectors between X & A and X & B respectively BECAUSE these lines meet at right angles.

even better, this dot product can be expressed with t as the only unknown and solved as a quadratic because X can be expressed solely in terms of t and thus the vectors XA and XB can be expressed in terms solely of t.

i have no idea how much of this makes sense to you, but the key is to set up this dot product IN TERSM OF THE PARAMETER t and WHICH WILL EQUAL zero.