8. Show that the points A (1,-2,-8), B (5, 0,-2) and C (11, 3, 7) are collinear and find the ratio in which B divides AC.

Answer

`B` divide ` AC` in `2:3`

Explanation

We are given that


`A=(1,-2,-8)`

`B=(5,0,-2)`

`C=(11,3,7)`


Since `A,B,C` are coliinear if


`|vec(AB)|+|vec(BC)|=|vec(AC)|`


`therefore vec(AB)=(5-1) hat i+(0+2) hat j+(-2+8) hat k=4 hat i+2 hat j+6 hat k`


`|vec(AB)|=sqrt((4)^2+(2)^2+(6)^2)`

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