Question 14 Find the coordinates of the point where the line (๐ฅ + 3)/3 = (๐ฆ โ 1)/(โ1) = (๐ง โ 5)/(โ5) cuts the XY Plane.
If line (๐ฅ + 3)/3 = (๐ฆ โ 1)/(โ1) = (๐ง โ 5)/(โ5) cuts the XY Plane
Then z = 0
So, let coordinates of point be (x, y, 0)
Now,
(๐ฅ + 3)/3 = (๐ฆ โ 1)/(โ1) = (๐ง โ 5)/(โ5) = k
Thus,
x = 3k โ 3, y = โk + 1, z = โ5k + 5
Since z = 0
โ5k + 5 = 0
5k = 5
k = 5/5
k = 1
Now,
x = 3k โ 3 = 3(1) โ 3 = 0
y = โk + 1 = โ1 + 1 = 0
Thus, Coordinates of Point are (0, 0, 0)

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.