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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(3, 2, 0), B(5, 3, 2), C(-9, 6, -3) are three points forming a triangle. If AD, the bisector of $\angle\text{BAC}$ meets BC in D then coordinates of D are:
  • ✓
    $\Big(-\frac {19}{8}, \frac {57}{16}, \frac {17}{16}\Big)$
  • B
    $\Big( \frac {19}{8}, -\frac {57}{16}, \frac {17}{16}\Big)$
  • C
    $\Big( \frac {19}{8}, \frac {57}{16}, \frac {17}{16}\Big)$
  • D
    None of these
✓

Answer

Correct option: A.
$\Big(-\frac {19}{8}, \frac {57}{16}, \frac {17}{16}\Big)$
According to question,
$\text{AB}=\sqrt{4+1+4}=3$
$\text{AC}=\sqrt{144+16+9}=13$
$\text{BD}:\text{DC}=\text{AB}:\text{AC}=3:13$
$\text{D}=\Big(\frac{3(-9)+13(15)}{3+13},\frac{3(6)+13(3)}{3+13},\frac{3(-3)+13(2)}{3+13}\Big)$
$=\Big(\frac{-38}{16},\frac{57}{16},\frac{17}{16}\Big)$
$\therefore\Big(-\frac {19}{8}, \frac {57}{16}, \frac {17}{16}\Big)$

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