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

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.

Text Solution

Verified by Experts

The equation of the line through the points A(3,4,1) and B(5,1,6) is given by
`(x-3)/(5-3)=(y-4)/(1-4)=(z-1)/(6-1) rArr (x-3)/2=(y-4)/-3=(z-1)/5`………..(i)
the equation of the XY-plane is z=0.
Since the line (i) meets the XY-plane, we have
`(x-3)/(2)=(y-4)/-3 = (0-1)/5 rArr (x-3)/2=-1/5` and `(y-4)/-3=-1/5`
`rArr x=(3-2/5)=13/5,y=(4+3/5)=23/5` and `z=0`.
Hence, the given line crosses the XY-plane at the point
`P(13/5,23/5,0)`.
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(5,1,1) 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 XZ plane.Also find the angle which this line makes with the XZ plane.

Find the equation of a plane passing through the points A(2,1,2) and B(4,-2,1) and perpendicular to plane vec(r ).(hat(i)-2hat(k))=5 . Also, find the coordinates of the point, where the line passing through the points (3,4,1) and (5,1,6) crosses the plane thus obtained.

The coordinates of the point where the line through the point A (5,1,6) and B(3,4,1) crosses the yz-plane is

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 coordinartes of the point where the line through (3,4,1) and (5,1,6) crosses xy-plane

Find the coordinate of the point P where the line through A(3,-4,-5) and B(2,-3,1) , crosses the plane passing through three points L(2,2,1),M(3,0,1) and N(4,-1,0) Also,find the ratio in which P divides the line segment AB.

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.