Question
A (3,2,0), B (5,3,2), C (-9,6,-3) are three points forming a triangle. AD , the bisector of angle BAC meets BC in D. Find the co-ordinates of D.
BITSAT
Mathematics
Pair of Lines
2024
BITSAT 2024 (Memory Based Paper 1)
BITSAT Mathematics Question (2024) — Solution
Options
- A. 19 8 , 57 15 , 57 15
- B. 19 8 , 57 16 , 17 16
- C. (2,3,0)
- D. (4,5,6)
Answer
B. 19 8 , 57 16 , 17 16
Step-by-step solution
Since A D is the bisector of B A C. BD DC = AB AC ....(i) Now, AB = (5-3)^2+(3-2)^2+(2-0)^2 = 4+1+4 = 9 =3 A C= (-9-3)^2+(6-2)^2+(-3-0)^2 = 144+16+9 =13 BD DC = 3 13 Hence, D divides BC in the ratio 3: 13 The co-ordinates of D are ( 3(-9)+13(5) 3+13 , 3(6)+13(3) 3+13 , 3(-3)+13(2) 3+13 ) = ( 19 8 , 57 16 , 17 16 )
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