Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
168 views
in 3D Coordinate Geometry by (42.5k points)
closed by

Find the ratio in which the line segment joining the points (4, 8, 10) and (6, 10, -8) is divided by the yz-plane.

1 Answer

+1 vote
by (44.7k points)
selected by
 
Best answer

Given: points A(4, 8, 10) and B(6, 10, -8) 

To find: the ratio in which the line joining given points is divided by the yz-plane 

Formula used:

Section Formula: 

A line AB is divided by C in m:n where A(x, y, z) and B(a, b, c).

 The coordinates of C is given by,

 \(\Big(\frac{nx+ma}{m+n},\frac{ny+mb}{m+n},\frac{nz+mc}{m+n}\Big)\) 

the x coordinate is always 0 on yz-plane 

Let Point C(0, y, z), and C divides AB in ratio k: 1 

Therefore, m = k and n = 1 

A(4, 8, 10) and B(6, 10, -8)

 

Coordinates of C using section formula:

On comparing:

\(\frac{6k+4}{k+1}\) = 0

⇒ 6k + 4 = 0(k + 1) 

⇒ 6k + 4 = 0 

⇒ 6k = – 4

⇒ k = \(\frac{-4}{6}\) 

⇒ k = \(\frac{-2}{3}\) 

Hence, C divides AB externally in ratio 2 : 3

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...