Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Three Dimensional Geometry

NDA 2021 · Mathematics · Three Dimensional Geometry

Consider the following statements : 1. A line in space can have...

Consider the following statements : 1. A line in space can have infinitely many direction ratios. 2. It is possible for certain line that the sum of the squares of direction cosines can be equal to sum of its direction cosines. Which of the above statements is/are correct?

Options

  1. A1 only
  2. B2 only
  3. CBoth 1 and 2
  4. DNeither 1 nor 2

Correct answer

C. Both 1 and 2

Step-by-step solution

There are infinitely many different line present in space with different direction ratios. So, statement 1 is correct ∴12+12+12=1+1+1\therefore 1^2+1^2+1^2=1+1+1 so, line have direction cosines 1,1,11,1,1. Such that sum of the squares of direction cosines can be equal to sum of its direction cosines.
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