Question
Find the coordinates of the point where the line through A(3, 4, 1) and B (5, 1, 6) crosses the x y-plane.
Solution
The line passes through the points A (3, 4, 1) and B (5, 1, 6)
where
are position vectors of A, B respectively.
Let
be the position vector of any point on the given line.
∴ the vector equation of the line is
or
...(1)
Let P (x, y, 0) be the point where the line AB crosses the x y-plane. Now P lies on (1)
...(2)
...(3)
...(4)
From (4),
From (2),
From (3),
point is 
where
are position vectors of A, B respectively.Let
be the position vector of any point on the given line.∴ the vector equation of the line is
or
...(1)Let P (x, y, 0) be the point where the line AB crosses the x y-plane. Now P lies on (1)
...(2) ...(3) ...(4)From (4),
From (2),
From (3),
point is 
