Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Three Dimensional Geometry

NDA 2023 · Mathematics · Three Dimensional Geometry

Paragraph: Consider two lines whose direction ratios are (2,-1,2)...

Paragraph: Consider two lines whose direction ratios are (2,−1,2)(2,-1,2) and (k,3,5)(k, 3,5). They are inclined at an angle π4\frac{\pi}{4}.
Question: What are the direction ratios of a line which is perpendicular to both the lines?

Options

  1. A(1,2,10)(1,2,10)
  2. B(−1,−2,10)(-1,-2,10)
  3. C(11,12,−10)(11,12,-10)
  4. D(11,2,−10)(11,2,-10)

Correct answer

D. (11,2,−10)(11,2,-10)

Step-by-step solution

Line perpendicular to both lines will be obtained by cross product of both =\left|i^j^k^2−12435\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k} \\ 2 & -1 & 2 \\ 4 & 3 & 5\end{array}\right|=-11 \hat{i}-2 \hat{j}+10 \hat{k} Direction Ratio : (−11,−2,10)(-11,-2,10) or (11,2,−10)(11,2,-10).
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