Q. 155.0( 1 Vote )

# Determine the poi

Given: Points A(2, 0, 3), B(0, 3, 2) and C(0, 0, 1)

To find: the point on yz-plane which is equidistant from the points

As we know x = 0 in yz-plane.

Let Q(0, y, z) any point in yz-plane

According to the question:

QA = QB = QC

QA2 = QB2 = QC2

Formula used:

The distance between any two points (a, b, c) and (m, n, o) is given by, Therefore,

The distance between Q(0, y, z) and A(2, 0, 3) is QA,   The distance between Q(0, y, Z) and B(0, 3, 2) is QB,  Distance between Q(0, y, z) and C(0, 0, 1) is QC,  As QA2 = QB2

4 + (z – 3)2+ y2 = (z – 2)2 + (y – 3)2

z2+ 9 – 6z + y2 + 4 = z2+ 4 – 4z + y2 + 9 – 6y

– 6z = – 4z – 6y

6y – 6z + 4z = 0

6y – 2z = 0

6y = 2z z = 3y…………………(1)

As QA2 = QC2

4 + (z – 3)2+ y2 = (z – 1)2 + y2

z2+ 9 – 6z + y2 + 4 = z2+ 1 – 2z + y2

13 – 6z = 1 – 2z

13 – 1 = 6z – 2z

4z = 12

z = 3

Put the value of z from (1):  y = 1

Hence point Q(0, 1, 3) in yz-plane is equidistant from A, B and C

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses RELATED QUESTIONS :

Determine the poiRD Sharma - Mathematics

Let (3, 4, -1) anRD Sharma - Mathematics

The length of theRD Sharma - Mathematics

If P (0, 1, 2), QRD Sharma - Mathematics

Show that the triMathematics - Exemplar

Write the length RD Sharma - Mathematics

If the distance bRD Sharma - Mathematics

Find the point onRD Sharma - Mathematics

Find the point onRD Sharma - Mathematics

Write the coordinRD Sharma - Mathematics