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
62 views
in Geometry by (96.4k points)
closed by
The plane which bisects the line segment joining the points (-3, -3, 4) and (3, 7, 6) at right angles, passes through which one of the following points?
1. (-2, 3, 5)
2. (4, -1, 7)
3. (2, 1, 3)
4. (4, 1, -2)

1 Answer

0 votes
by (85.7k points)
selected by
 
Best answer
Correct Answer - Option 4 : (4, 1, -2)

From question, let’s assume the points, A(-3, -3, 4) and B(3, 7, 6).

The midpoint of A and B is:

\(⇒ P\left( {\frac{{ - 3 + 3}}{2},\frac{{ - 3 + 7}}{2},\frac{{4 + 6}}{2}} \right) = P\left( {0,2,5} \right)\)

The required plane is perpendicular bisector of line joining A and B. So direction ratios of normal to the plane is proportional to the direction ratios of line joining A and B.

The direction ratios of AB is:

⇒ 3 + 3, 7 + 3, 6 - 4

⇒ 6, 10, 2

The equation of plane is given by the formula:

a(x - x1) + b(y - y1) + c(z - z1) = 0

On substituting point ‘P’,

⇒ 6(x - 0) + 10(y - 2) + 2(z - 5) = 0

[∴ p(0, 2, 5) line on the plane]

∴ 3x + 5y - 10 + z - 5 = 0

⇒ 3x + 5y + z = 15

On checking all the options,

The point (4, 1, -2) in option (d) satisfies the above equation. So, option (d) is the correct answer.

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

...