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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: If P(x,y,z)P(x, y, z) is any point on the sphere, then what is PA2+PB2P A^2+P B^2 equal to?

Options

  1. A1515
  2. B1414
  3. C1313
  4. D6.56.5

Correct answer

B. 1414

Step-by-step solution

∵∠APB=90∘∴PA2+PB2=AB2=(2−1)2+(1+1)2+(−1−2)2=1+4+9=14\because \angle A P B=90^{{}^{\circ}}\therefore \quad P A^2+P B^2=A B^2=(2-1)^2+(1+1)^2+(-1-2)^2=1+4+9=14
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