Let A and B are the points which trisect the line segment joining the points P(4,2,-6) and Q(10,-16,6)

The point A divides the line segment PQ in the ratio of 1:2.

Using section formula,

A (x,y,z) = \(( \dfrac{1(10)+2(4)}{1+2}, \dfrac{1(-16)+2(2)}{1+2},\)

\( \dfrac{1(6)+2(-4)}{1+2}) \)

A(x,y,z) = (6,-4,-2)

Similarly, the point B divides the line segment PQ in the ratio of 2:1.

B(x,y,z) = \( ( \dfrac{2(10)+1(4)}{1+2}, \dfrac{2(-16)+1(2)}{1+2}, \)

\( \dfrac{2(6)+1(-4)}{1+2}) \)

B(x,y,z)=(8,-10,2)

Therefore, the point (6,-4,-2) and (8,-10,2) are the points which trisect the line segment joining the points P(4,2,-6) and Q(10,-16,6) .

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