Find the co-ordinates of the points of trisection of the line segment joining the points A(2, -3, 5) and B(6, 0, -1).

Answer

N/a

Explanation

Let C(x,y,z) and D(a,b,c) trisect AB.
`therefore C` divides the line segment AB in the ration 1 : 2.
Therefore, `x=(1xx6+2xx2)/(1+2)=(10)/(3)`
`y=(1xx0+2xx(-3))/(1+2)= -2`
`z=(1xx(-1)+2xx5)/(1+2)= 3`

Similarly, D divides the line segment AB in the ration 2 : 1.
`a=(2xx6+1xx2)/(2+1)=-(14)/(3)`
`b=(2xx0+1xx(-3))/(2+1)= -1`
`c=(2xx(-1)+1xx5)/(2+1)=1`
`therefore` Co-ordinates of the points of trisection are `C((10)/(3),-2,3) " and" D((14)/(3),-1, 1)`