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Question: The points (3, 2, 0), (5, 3, 2) and (–9, 6, –3), are the vertices of a triangle ABC. AD is the inter...

The points (3, 2, 0), (5, 3, 2) and (–9, 6, –3), are the vertices of a triangle ABC. AD is the internal bisector of ŠBAC which meets BC at D, then the co-ordinates of D, are

A

(1716,5716,198)\left( \frac{17}{16},\frac{57}{16},\frac{19}{8} \right)

B

(198,5716,1716)\left( \frac{19}{8},\frac{57}{16},\frac{17}{16} \right)

C

(0,0,1716)\left( 0,0,\frac{17}{16} \right)

D

(1716,0,0)\left( \frac{17}{16},0,0 \right)

Answer

(198,5716,1716)\left( \frac{19}{8},\frac{57}{16},\frac{17}{16} \right)

Explanation

Solution

AB =4+1+4\sqrt{4 + 1 + 4} = 3

AC = 144+16+9\sqrt{144 + 16 + 9}= 13

D(27+653+13,18+393+13,9+263+13)D\left( \frac{–27 + 65}{3 + 13},\frac{18 + 39}{3 + 13},\frac{- 9 + 26}{3 + 13} \right)=(198,5716,1716)\left( \frac{19}{8},\frac{57}{16},\frac{17}{16} \right)