Q. 75.0( 3 Votes )

# Find the points o

Answer :

Given: Points A(1, 2, 3)

To find: the point on z-axis which is at distance of from the given point

As we know x = 0 and y = 0 on z-axis

Let R(0, 0, z) any point on z-axis

According to question: RA2 = 21

Formula used:

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

Distance between R(0, 0, z) and A(1, 2, 3) is RA,   As RA2 = 21

5 + (z – 3)2 = 21

z2+ 9 – 6z + 5 = 21

z2 – 6z = 21 – 14

z2– 6z – 7 = 0

z2– 7z + z – 7 = 0

z(z– 7) + 1(z – 7) = 0

(z– 7) (z + 1) = 0

(z– 7) = 0 or (z + 1) = 0

z= 7 or z = -1

Hence points (0, 0, 7) and (0, 0, -1) on z-axis is equidistant from (1, 2, 3)

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

The length of theRD 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