NDA2024MathematicsThree Dimensional GeometryActual

Paragraph: Let 2 x^2+2 y^2+2 z^2+3 x+3 y+3 z-6=0 be a sphere. Question: What is the diameter of the sphere?

Options

A5 3 4
B5 3 2
C3 5 4
D3 5 2

Correct answer

B. 5 3 2

Step-by-step solution

(b) Given sphere : 2 x^2+2 y^2+2 z^2+3 x+3 y+3 z-6=0 ....(i) Divide equation (1) by (2) x^2+y^2+z^2+ 3 2 x+ 3 2 y+ 3 2 z-3=0 aligned & radius of sphere = ( 3 4 )^2+ ( 3 4 )^2+ ( 3 4 )^2+3 = 27 16 +3 = 75 4 & radius = 5 3 4 & Diameter of sphere = 5 3 2 aligned

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 ? 2026 Passage: 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 ? 2026 Passage: 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 . 2026 Passage: 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 2026 Passage: 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 ? 2026 Passage: 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 ? 2026 For 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 2025 For 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