Home
Class 12
MATHS
Find the coordinates of the point whe...

Find the coordinates of the point where the line through the points `A(3,\ 4,\ 1)a n d\ B(5,\ 1,\ 6)` crosses the XY-plane.

Text Solution

Verified by Experts

Here, we are given points `A(3,4,1)` and `B(5,1,6)`.
So, direction ratio of line `AB = (2,-3,5)`.
So, equation of line becomes,
`(x-3)/2 = (y-4)/-3 = (z-1)/5 = k`
`=>(z-1)/5 = k`
As the line is crossing XY-plane, z-coordinate will be `0`. So, `(0-1)/5 = k => k = -1/5`
`:. (x-3)/2 = -1/5 => x = 3-2/5 = 13/5`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the coordinates of the point where the line through the points A (3, 4, 1) and B(5, 1, 6) crosses the XY-plane.

Find the coordinates of the point where the line through the points A (3, 4, 1) and B (5, 1, 6) crosses the XY-plane.

Find the coordinates of the point where the line through the points A(3,4,1) and B(5,1,6) crosses the X Z plane. Also find the angle which this line makes with the X Z plane.

Find the coordinates of the point where the line through the points (3, – 4, – 5) and (2, – 3, 1), crosses the plane determined by the points (1, 2, 3), (4, 2, – 3) and (0, 4, 3).

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

Find the coordinates of the point where the line through (3, 4, 5) and (2, 3, 1) crosses the plane 2x + y + z = 7 .

Find the coordinates of the point where the line through (3, -4, -5) and (2, -3, 1) crosses the plane 2x + y + z = 7 .

Find the coordinates of the point where the line joining the points (1, -2, 3) and (2, -1, 5) cuts the plane x-2y + 3z= 19 . Hence, find the distance of this point from the point (5,4,1)

Find the coordinates of the point where the line through (3, –4, –5) and (2, –3, 1) crosses the plane determined by points A(1, 2, 3), B(2, 2, 1) and C (-1, 3,6)

Find the coordinate of the point where the line through (5, 1, 6) and (3, 4, 1) crosses the i. yz-plane ii. zx-plane.