Find the ratio in which the line segment joining the point A(2,1,5) and B(3,4,3) is divided by the plane 2x+2y-2z=1 - Maths - Introduction to Three Dimensional Geometry

Question

Find the ratio in which the line segment joining the point
A(2,1,5) and B(3,4,3) is divided by the plane 2x+2y-2z=1 Also find
the coordinates Please answer quickly! i have an exam tomorrow!

Rayya Halim · Accepted Answer

Suppose that the line AB, joining the points A (2, 1, 5)
and B(3, 4, 3) is divided by the plane 2x+2y-2z = 1 at the
point
p( a,b,c) in the ratio k: 1, internally Then the
coordinates of p are
a=3k+2/1+k , b=4k+1/k+1 , and c= 3k+5/k+1
and p(a, b, c) lies on the plane 2x+2y-2z=1
so we have
2(3k+1/k+1) + 2(4k+1/k+1) -2 ( 3k+5/k+1) = 0
âˆ´ k = 3/4
Now a = 17/ 7
b =16 / 7
c = 29/7

Find the ratio in which the line segment joining the point A(2,1,5) and B(3,4,3) is divided by the plane 2x+2y-2z=1. Also find the coordinates. Please answer quickly! i have an exam tomorrow!