Question:
Find the equation of the set of points which are equidistant from the points (1, 2, 3) and (3, 2, –1).
Find the equation of the set of points which are equidistant from the points (1, 2, 3) and (3, 2, –1).
Updated On: Oct 23, 2023
Hide Solution
Verified By Collegedunia
Solution and Explanation
Let P (x, y, z) be the point that is equidistant from points A(1, 2, 3) and B(3, 2, -1).
Accordingly, PA = PB
⇒ PA2 = PB2
⇒(x-1)2+(y-2)2 +(z−3)2 = (x−3)2+(y−2)2 +(z+1)2
⇒ x2 - 2x + 1+ y2 - 4y+4+z2 - 6z + 9 = x2 - 6x+9+ y2 - 4y+ 4 + z2+2z+1
⇒ - 2x - 4y - 6z +14= - 6x - 4y+ 2z+14
⇒ - 2x - 6z + 6x - 2z = 0
⇒ 4x - 8z = 0
⇒x - 2z= 0
Thus, the required equation is x - 2z = 0.
Accordingly, PA = PB
⇒ PA2 = PB2
⇒(x-1)2+(y-2)2 +(z−3)2 = (x−3)2+(y−2)2 +(z+1)2
⇒ x2 - 2x + 1+ y2 - 4y+4+z2 - 6z + 9 = x2 - 6x+9+ y2 - 4y+ 4 + z2+2z+1
⇒ - 2x - 4y - 6z +14= - 6x - 4y+ 2z+14
⇒ - 2x - 6z + 6x - 2z = 0
⇒ 4x - 8z = 0
⇒x - 2z= 0
Thus, the required equation is x - 2z = 0.
Was this answer helpful?
0
0
Top Questions on distance between two points
- Let the line passing through the points \( (-1, 2, 1) \) and parallel to the line \[ \frac{x - 1}{2} = \frac{y + 1}{3} = \frac{z}{4} \] intersect the line \[ \frac{x + 2}{3} = \frac{y - 3}{2} = \frac{z - 4}{1} \] at the point P. Then the distance of P from the point Q(4, -5, 1) is:
- JEE Main - 2025
- Mathematics
- distance between two points
- You measure two quantities as \( A = 1.0 \,m \pm 0.2 \,m \), \( B = 2.0 \,m \pm 0.2 \,m \). We should report the correct value for \( \sqrt{AB} \) as:
- BITSAT - 2024
- Physics
- distance between two points
- There are 20 lines numbered as 1,2,3,..., 20. And the odd numbered lines intersect at a point and all the even numbered lines are parallel. Find the maximum number of point of intersections
- JEE Main - 2024
- Mathematics
- distance between two points
- The efficiency of a Carnot engine operating between steam point and ice point is:
- KEAM - 2024
- Physics
- distance between two points
- \(L_1: γ^-=(i+2j+3k)+λ(i-j+k)\);
\(L_2: γ^-=(4i+5j+6k)+μ(i+j-k)\),
intersect \(L_1\) and \(L_2\) at P and Q respectively. If \((α, β, γ)\) is the mid point of the line segment PQ, then \(2(α, β, γ\)) is equal to- JEE Main - 2024
- Mathematics
- distance between two points
View More Questions
Questions Asked in CBSE Class XI exam
- If U = {a, b, c, d, e, f, g, h}, find the complements of the following sets:
(i) A = {a, b, c}
(ii) B = {d, e, f, g}
(iii) C = {a, c, e, g}
(iv) D = {f, g, h, a}- CBSE Class XI
- Complement of a Set
- Consider the following species: N3- , O2-, F-, Na+, Mg2+ and Al3+
- What is common in them?
- Arrange them in the order of increasing ionic radii.
- CBSE Class XI
- Modern Periodic Law And The Present Form Of The Periodic Table
- Find and write down structures of 10 interesting small molecular weight biomolecules. Find if there is any industry which manufactures the compounds by isolation. Find out who are the buyers.
- CBSE Class XI
- How To Analyse Chemical Composition?
- How many litres of water will have to be added to 1125 litres of the 45% solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid content?
- CBSE Class XI
- inequalities
Find the mean and variance for the following frequency distribution.
Classes 0-10 10-20 20-30 30-40 40-50 Frequencies 5 8 15 16 6 - CBSE Class XI
- Variance and Standard Deviation
View More Questions