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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Three Dimensional Geometry

NDA 2023 · Mathematics · Three Dimensional Geometry

Paragraph: Let A(1,-1,2) and B(2,1,-1) be the end points of the...

Paragraph: Let A(1,−1,2)A(1,-1,2) and B(2,1,−1)B(2,1,-1) be the end points of the diameter of the sphere x2+y2+z2+2ux+2vy+2wz−1=0x^2+y^2+z^2+2 u x+2 v y+2 w z-1=0
Question: What is u+v+wu+v+w equal to?

Options

  1. A−2-2
  2. B−1-1
  3. C11
  4. D22

Correct answer

A. −2-2

Step-by-step solution

A(1,−1,2),B(2,1,−1)A(1,-1,2), B(2,1,-1) Centre of sphere =(−u,−v,−w)=(-u,-v,-w) Centre is mid point of AB(−u,−v,−w)=(1+22,−1+12,2−12)=(32,0,12)∴u=−32,v=0,w=−12u+v+w=−32+0−12=−2A B(-u,-v,-w)=\left(\frac{1+2}{2}, \frac{-1+1}{2}, \frac{2-1}{2}\right)=\left(\frac{3}{2}, 0, \frac{1}{2}\right)\therefore \quad u=\frac{-3}{2}, v=0, w=\frac{-1}{2}u+v+w=\frac{-3}{2}+0-\frac{1}{2}=-2
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