Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA2017MathematicsThree Dimensional GeometryActual

If , and are the angles which the vector OP (O being the origin) makes with positive direction of the coordinate axes, then which of the following are correct? 1. ^2 + ^2 = ^2 2. ^2 + ^2 = ^2 3. ^2 + ^2 + ^2 =2 Select the correct answer using the code given below.

Options

  1. A1 and 2 only
  2. B2 and 3 only
  3. C1 and 3 only
  4. D1,2 and 3

Correct answer

C. 1 and 3 only

Step-by-step solution

We know, ^2 + ^2 + ^2 =1 ^2 + ^2 =1- ^2 = ^2 Statement 1 is correct. Now, ^2 + ^2 + ^2 =1 aligned & 1- ^2 +1- ^2 +1- ^2 =1 & 3- ( ^2 + ^2 + ^2 )=1 & ^2 + ^2 + ^2 =2 aligned Statement 3 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 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