Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Three Dimensional Geometry

NDA 2017 · Mathematics · Three Dimensional Geometry

The points P(3,2,4), Q(4,5,2), R(5,8,0) and S(2,-1,6) are

The points P(3,2,4),Q(4,5,2),R(5,8,0)\mathrm{P}(3,2,4), \mathrm{Q}(4,5,2), \mathrm{R}(5,8,0) and S(2,−1,6)\mathrm{S}(2,-1,6) are

Options

  1. Avertices of a rhombus which is not a square
  2. Bnon-coplanar
  3. Ccollinear
  4. Dcoplanar but not collinear

Correct answer

C. collinear

Step-by-step solution

P(3,2,4),Q(4,5,2),R(5,8,0),S(2,−1,6)PQ=(4−3)2+(5−2)2+(2−4)2=1+9+4=14QR=(5−4)2+(8−5)2+(0−2)2=1+9+4=14RS=(2−5)2+(−1−8)2+(6−0)2=9+81+36=126=314PS=(2−3)2+(−1−2)2+(6−4)2=1+9+4=14\begin{aligned} & P(3,2,4), Q(4,5,2), R(5,8,0), S(2,-1,6) \\ & P Q=\sqrt{(4-3)^2+(5-2)^2+(2-4)^2} \\ & =\sqrt{1+9+4}=\sqrt{14} \\ & Q R=\sqrt{(5-4)^2+(8-5)^2+(0-2)^2} \\ & =\sqrt{1+9+4}=\sqrt{14} \\ & R S=\sqrt{(2-5)^2+(-1-8)^2+(6-0)^2} \\ & =\sqrt{9+81+36}=\sqrt{126}=3 \sqrt{14} \\ & P S=\sqrt{(2-3)^2+(-1-2)^2+(6-4)^2} \\ & =\sqrt{1+9+4}=\sqrt{14}\end{aligned}
Since, PQ+QR+PS=RS\mathrm{PQ}+\mathrm{QR}+\mathrm{PS}=\mathrm{RS}, points are collinear.
Practice Three Dimensional Geometry on Quantrex Academy →

More from Three Dimensional Geometry

Passage: The equation of the sphere S is x^2+y^2+z^2-4x-6y-12z+k=0 . Question: If the… NDA 2026Passage: A line L passing through the point (-1,2,-3) is perpendicular to the plane P… NDA 2026Passage: P(-2,-3,5) , Q(4,-1,5) , R(6,-4,8) and S(2,-6,10) are four points. Question… NDA 2026Passage: A line L passing through the point (-1,2,-3) is perpendicular to the plane P… NDA 2026Passage: P(-2,-3,5) , Q(4,-1,5) , R(6,-4,8) and S(2,-6,10) are four points. Question… NDA 2026Passage: The equation of the sphere S is x^2+y^2+z^2-4x-6y-12z+k=0 . Question: What is… NDA 2026For the following two (02) items: A plane P is parallel to the line having direction… NDA 2025For the following two (02) items: Suppose S is the sphere with the smallest radius that… NDA 2025A(1, 2, -1) , B(2, 5, -2) and C(4, 4, -3) are three vertices of a rectangle. What is the… NDA 2025If a line (x+1)/(p) = (y-1)/(q) = (z-2)/(r) where p = 2q = 3r , makes an angle θ with the… NDA 2025What is the equation of the plane passing through the point (1, 1, 1) and perpendicular… NDA 2025For the following two (02) items: Let A(1, -1, 0) , B(-2, 1, 8) and C(-1, 2, 7) are three… NDA 2025For the following two (02) items: Suppose S is the sphere with the smallest radius that… NDA 2025If a line in 3 dimensions makes angles α , β and γ with the positive directions of the… NDA 2025A line makes angles α , β and γ with the positive directions of the coordinate axes. If a… NDA 2025For the following two (02) items: A plane P is parallel to the line having direction… NDA 2025 Full Three Dimensional Geometry list Three Dimensional Geometry JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs