Q211 / 270 · NDA 2023 (Phase 1) · Mathematics

Paragraph: Let $A(1,-1,2)$ and $B(2,1,-1)$ be the end points of the diameter of the sphere $x^2+y^2+z^2+2 u x+2 v y+2 w z-1=0$
Question: What is $u+v+w$ equal to?

  • Correct answer
    A
    $-2$
  • B
    $-1$
  • C
    $1$
  • D
    $2$

Solution

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

Hence, the correct answer is option: 'A'.

Relevant Questions