Dear forum members, I don't understand why I am getting the wrong answer
A line goes through the points (1,-3,1) and (13,-12,4). Does it cross the x-axis? If so, at what point?
I call the points A and P, respectively. I form the direction vector AP, which becomes ( -4 -5 -1) (sorry for the nonstandard vector representation, please pretend this is a column).
The equation of the line is then
r=(1,-3,1) +t(-4 -5 -1)
I know that at the point where the line crosses the x-axis, the y and z -coordinates are zero.
y and z must equal zero, so I solve for t to see whether it will be the same for both. I get
for y t=-3/5
for z t=1
Hence, I would conclude that the line does not cross the x-axis, but the answer in my book says it does. Please help me find, where I went wrong.
Thank you. All help is much appreciated.