Question

Find the ratio in which the line joining the points (2,4,16) and (3,5,-4) is divided by the plane 2x-3y+z+6=0.also find the coordinates of the point of division

Answer 1

Answer:

R=x−24–2=y+13+1=z−42–4  

R=x−22=y+14=z−4−2=x−2+y+1+z−42+4–2=x+y+z−54=3−54=−12

So the line segment is divided externally in the ratio 1:2

Then R=x−22=−12=x−12−2=x−10→x=1

R=y+14=−12=y+1+24−4→y=−3

R=z−4−2=−12=z−4−1−2+2→z=4

(1,-3,4) is the intersection point.

,……………………………………………………………………………..

Alternately the ratio can be found out by

[math]R=\dfrac {y+z+x-3|_{(2,-1,4)}}{y+z+x-3|_{(4,3,2)}[/math]

=−2–1+4−34+3+2−3

=−13

Step-by-step explanation: