Question

A (5,4,6), B (1,-1,3), C (4,3,2) are three points. Find the coordinates of the point in which the
bisector of angle BAC meets the side BC​

Answer 1

Answer:

Sol:

A(1,2,3) , B(0,4,1) C (-1,-1,-3) are the vertices of a triangle ABC

AB = √[(0 -1)2 + (4 - 2)2 + (1 - 3)2 ] = √ ( 1 + 4 + 4)

AB = 3.

AC = √[(-1 -1)2 + (-1 - 2)2 + (-3- 3)2 ] = √ ( 4 + 9 + 36)

AC = 7.

Since bisector of ∠BAC meets BC in D .

AD is the bisector of ∠BAC we have BD/DC = AB / AC = 3 / 7.

D divides BC in the ratio 3 : 7 .

Hence the coordinates of D are = [ (-3 +0) / 10 , (-3 + 28) / 10 , ( -9 +7) / 10 ]

D = [ -3 / 10 , 5 / 2 , -1 / 5 ]