Find co-ordinate of the point where the line through (3, 4, 1) and (5,

1.	Find co-ordinate of the point where the line through (3, 4, 1) and (5, 1, 6) crosses xy-plane.
Answer» Let A = (3, 4, 1) and B = (5, 1, 6) Then direction ratio of line AB are 3 - 5, 4 - 1, 1 - 6, = (-2, 3 ,5) So, Equation of any line AB will be (x - 3)/-2 = (y - 4)/3 = (z - 1)/-5 = r (Let) Co-ordinate of any point P of above line is P(-2r + 3, 3r + 4, -5r + 1) . If p lies on xy plane, then -5r + 1 = 0 r = 1/5 ∴ co-ordinate require is (13/5,23/5,0)

Find co-ordinate of the point where the line through (3, 4, 1) and (5, 1, 6) crosses xy-plane.

Answer»

Let A = (3, 4, 1) and B = (5, 1, 6)

Then direction ratio of line AB are 3 - 5, 4 - 1, 1 - 6,

= (-2, 3 ,5)

So, Equation of any line AB will be

(x - 3)/-2 = (y - 4)/3 = (z - 1)/-5 = r (Let)

Co-ordinate of any point P of above line is

P(-2r + 3, 3r + 4, -5r + 1) .

If p lies on xy plane, then -5r + 1 = 0

r = 1/5

∴ co-ordinate require is (13/5,23/5,0)