# Find the vector equation of the line AB and find the points where the line intersects the coordinate planes.

The position vectors of the points A and B are (1,4,6) and (3,4,7), re- spectively. Find the vector equation of the line AB and find the points where the line intersects the coordinate planes.

The answer for the first part corresponds to (1,4,6) +t(2,0,1).However i cant figure out the answer for the second part.

First note that the equation is NOT $$(1,4,6) +t(2,0,1)$$, because this is not an equation. The equation is $$(x,y,z)=(1,4,6) +t(2,0,1)\ .$$ One of the coordinate planes is given by $$z=0$$. Using this together with the equation of the line you can find the corresponding value of $$t$$ and then this gives you the point of intersection. Do the same for the other coordinate planes.