Given point A(-4,2,3) and B(4,0,1) what conditions is the line: [x,y,z] = [4,0,1] + t[m,n,1] perpendicular to AB? Then determine a vector equation either in terms of m or n, of the line that satisfies the condition.

Attempt:

AB = [8,-2,-2]

Therefore, the dot product of [8,-2,-2] and [m,n,1] must be zero.

8m-2n -2 = 0

To find the direction vector of the new vector equation they are asking for, should i take cross product of AB and [m,n,1]

and then do it all in terms of n or m, using 8m-2n-2 = 0?

Thank you!
Yes, your answer is correct....
Yes, your answer is correct....