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Let ` vec a , vec b , vec c` be the position vectors of three distinct points A, B, C. If there exist scalars x, y, z (not all zero) such that `x vec a+y vec b+z vec c=0a n dx+y+z=0,` then show that `A ,Ba n dC` lie on a line.

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Verified by Experts

Given, a, b and c are all distict points.
It means all lie in a straight line
Say point c divides the line in a ratio `y = x`
Therefore, using section formula,
`c = (yb+xa)/(y+x)`
...
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