Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA2023MathematicsThree Dimensional GeometryActual

Paragraph: Let a vector a =4 i -8 j +k make angles , , with the positive directions of x, y, z axes respectivelv, Question: What is equal to?

Options

  1. A1 3
  2. B4 9
  3. C5 9
  4. D2 3

Correct answer

B. 4 9

Step-by-step solution

a =4 i -8 j + k If angle made with X axis = =l= a₁ a₁^2+a₂^2+a₃^2 = 4 4^2+(-8)^2+(1)^2 = 4 9

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 radius of the sphere S is 8 units, what is the value of k ? 2026Passage: A line L passing through the point (-1,2,-3) is perpendicular to the plane P given by 2x+3y+z+5=0 . Question: What is the equation of the line L ? 2026Passage: P(-2,-3,5) , Q(4,-1,5) , R(6,-4,8) and S(2,-6,10) are four points. Question: Consider the following statements : I. PQ is parallel to RS . II. PR is perpendicular to QS . 2026Passage: A line L passing through the point (-1,2,-3) is perpendicular to the plane P given by 2x+3y+z+5=0 . Question: What are the direction ratios of a line M parallel to the pla 2026Passage: P(-2,-3,5) , Q(4,-1,5) , R(6,-4,8) and S(2,-6,10) are four points. Question: What is (PQ^2+2QS^2-2PR^2) equal to ? 2026Passage: The equation of the sphere S is x^2+y^2+z^2-4x-6y-12z+k=0 . Question: What is the radius of the sphere passing through origin and concentric with the sphere S ? 2026For the following two (02) items: A plane P is parallel to the line having direction ratios 1, 3, 2 and contains the line of intersection of the planes 6x + 4y - 5z = 2 and x - 2y 2025For the following two (02) items: Suppose S is the sphere with the smallest radius that passes through the points A(1, 0, 0) , B(0, 1, 0) and C(0, 0, 1) . On which one of the follo 2025 Full Three Dimensional Geometry list All NDA PYQs