Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2015
Exam
NDA
Year
2015
Subject
Mathematics
Chapter
Three Dimensional Geometry

NDA 2015 · Mathematics · Three Dimensional Geometry

From the point P(3,-1,11) , a perpendicular is drawn on the line L...

From the point P(3,−1,11)P(3,-1,11), a perpendicular is drawn on the line LL given by the equation x2=y−23=z−34\frac{x}{2}=\frac{y-2}{3}=\frac{z-3}{4}. Let QQ be the foot of the perpendicular. What is the length of the line segment PQ?

Options

  1. A47\sqrt{47} units
  2. B7 units
  3. C53\sqrt{53} units
  4. D8 units

Correct answer

C. 53\sqrt{53} units

Step-by-step solution

Now x2−x1=−1\mathrm{x}_2-\mathrm{x}_1=-1x2−3=−1∴x2=2\begin{array}{ll} & \mathrm{x}_2-3=-1 \\ \therefore \quad & \mathrm{x}_2=2 \end{array}Similarly,Similarly,y2−y1=6y2+1=6∴y2=5 and z2−z1=−4z2−11=−4z2=−4+11=7\begin{array}{ll}& \mathrm{y}_{2}- \mathrm{y}_{1}=6 \\ & \mathrm{y}_{2}+1=6 \\ \therefore \quad & \mathrm{y}_{2}=5 \\ \text{ and }& \mathrm{z}_{2}- \mathrm{z}_{1}=-4 \\ & \mathrm{z}_{2}-11=-4 \\ & \mathrm{z}_{2}=-4+11=7 \end{array}∴\therefore \quad Co-ordinate of QQ is (2,5,7)∴(2,5,7)\therefore \quad Length of segment PQ =(2−3)2+(5+1)2+(7−11)2=1+36+16=53 units. \begin{aligned} & =\sqrt{(2-3)^2+(5+1)^2+(7-11)^2} \\ & =\sqrt{1+36+16}=\sqrt{53} \text{ units. } \end{aligned}\therefore \quad$ Option (C) is correct.
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