Question:
A(3, 2, 0), B(5, 3, 2) and C(-9, 6, -3) are the vertices of a triangle ABC. If the bisector of ∠BAC meets BC at D, then coordinates of D are
A(3, 2, 0), B(5, 3, 2) and C(-9, 6, -3) are the vertices of a triangle ABC. If the bisector of ∠BAC meets BC at D, then coordinates of D are
Options:
- (-19/8, 57/16, 17/16)
- (-19/8, -57/16, 17/16)
- (19/8, 57/16, 17/16)
- (19/8, -57/16, 17/16)
- (-19/8, 57/16, 17/16)
- (-19/8, -57/16, 17/16)
- (19/8, 57/16, 17/16)
- (19/8, -57/16, 17/16)
Correct Answer: a)
Explanation:
ADis bisector of ZBAC
= Ratio at Dis c : b, where
c=AB=,/(3-5 + (2-3) + (0-2)
‘ =VI+1+4=+9=3
b=AC=,/3+97 + (2-6) + (0+3) !
=y144 +16 +9 =+√169=13
A(3.2.0)
1 AN
1 c &)
4 A
a
¥ cb \
B(5.3,2) D C(-9,6,-3)
‘ .. For point D:
x= E940) _ 394136) 3s _ 19
c+b – 3+13 16 ~ 8
hon a
_ c(6)+b(3) _ 3(6)+13(3) _ 57
YT TT 3m 16
— 3462) _ 3(=3)+13(2) _ 17
ZT Te TT 313 C16
; io (19 57 17
‘ Hence, point D is (%, bg) 1)
169.
‘ @al+bm+cn=0
!
ADis bisector of ZBAC
= Ratio at Dis c : b, where
c=AB=,/(3-5 + (2-3) + (0-2)
‘ =VI+1+4=+9=3
b=AC=,/3+97 + (2-6) + (0+3) !
=y144 +16 +9 =+√169=13
A(3.2.0)
1 AN
1 c &)
4 A
a
¥ cb \
B(5.3,2) D C(-9,6,-3)
‘ .. For point D:
x= E940) _ 394136) 3s _ 19
c+b – 3+13 16 ~ 8
hon a
_ c(6)+b(3) _ 3(6)+13(3) _ 57
YT TT 3m 16
— 3462) _ 3(=3)+13(2) _ 17
ZT Te TT 313 C16
; io (19 57 17
‘ Hence, point D is (%, bg) 1)
169.
‘ @al+bm+cn=0
!