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INTRODUCTION TO THREE DIMENSIONAL GEOMETRY — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSINTRODUCTION TO THREE DIMENSIONAL GEOMETRY1 Mark
MCQ
A = (1, 1, 4) and B = (5, -3, 4) are two points. If the points P, Q are on the line AB such that AP = PQ = QB then PQ =
  • A
    $2\sqrt{2}$
  • B
    $4$
  • ✓
    $\sqrt{\frac{32}{9}}$
  • D
    $\sqrt{2}$
✓

Answer

Correct option: C.
$\sqrt{\frac{32}{9}}$
$\text{AB}=\sqrt{(1-5)^2+(1+3)^2+(4+4)^2}$
$\text{AB}=\sqrt{(-4)^2+4^2}$
$\text{AB}=\sqrt{32}$
$\text{AB}=3\times\text{PQ},=\frac{\sqrt{132}}{3}=\sqrt{\frac{32}{9}}$

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