Download App

Introduction To 3D Coordinate Geometry — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSIntroduction To 3D Coordinate Geometry3 Marks
Question
Find the point on y-axis which is equidistant from the points (3, 1, 2) and (5, 5, 2).
✓

Answer

Let P(0, y, 0) be a point on y-axis which is equidistant from Q(3, 1, 2) and R(5, 5, 2).

So

(PR)2 = (PQ)2 ⇒ (0 - 5)2 + (y - 5)2 + (0 - 2)2 = (0 - 3) + (y - 1)2 + (0 + 2)2 

⇒ 25 + y2 + 25 - 10y + 4 = 9 + y2 + 1 - 2y + 4

⇒ -10y + 2y = 14 - 54

⇒ -14z - 8z = 16 - 49

⇒ -8y = -40

⇒ y = 5

so, the required point is (0, 5, 0)

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Introduction To 3D Coordinate Geometry→Introduction To 3D Coordinate Geometry — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

Find the probability that when a hand of 7 cards is drawn from a well shuffled deck of 52 cards, it contains
  1. all Kings
  2. 3 Kings
  3. at least 3 Kings
→
Evaluate $(\sqrt{3}+\sqrt{2})^{6}-(\sqrt{3}-\sqrt{2})^{6}$.
→
In an A.P., show that $\text{a}_{\text{m}+\text{n}}+\text{a}_{\text{m}-\text{n}}=2\text{a}_\text{m}.$
→
Find the distance of the line 4x + 7y + 5 = 0 from the point (1, 2) along the line 2x - y = 0
→
Planes are drawn parallel to the coordinate planes through the points (3, 0, -1) and (-2, 5, 4).
Find the lengths of the edges of the parallelopiped so formed.
→
Find the equation of the ellipse with axes as the axes of coordinates having latus rectum 5 and eccentricity $e=\frac{2}{3}$.
→
Show that $\lim\limits_{\text{x}\rightarrow2^-}\ \frac{\text{x}}{[\text{x}]}\ne\lim\limits_{\text{x}\rightarrow2^+}\frac{\text{x}}{[\text{a}]}.$
→
Express the complex number $\left(-2-\frac{1}{3} i\right)^3$ in the form of $a+i b$.
→
If $\frac{\text{(2n!)}}{3!(2\text{n}-3)!}$ and $\frac{\text{n!}}{2!(2\text{n}-2)!}$ are in the ratio 44 : 3 find n.
→
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}(\text{cosec x}-\cot\text{x})$
→