Find the coordinates of the points which trisect the line segment joining the points $$P(4$$,$$2$$, $$-$$ $$6)$$ and $$Q(10$$, $$-$$ $$16$$,$$6)$$.

Question

Infinity Learn · Accepted Answer

Let the point $$R1$$, trisects the line PQ i.e., it divides the line in the ratio $$1$$:$$2$$⇒$$R1=1$$×$$10+2$$×$$41+2$$,$$1$$×$$($$−$$16)+2$$×$$21+2$$,$$1$$×$$6+2$$×$$($$−$$6)1+2=10+83$$,−$$16+43$$,$$6$$−$$123=183$$,−$$123$$,−$$63=(6$$,−$$4$$,−$$2)Again$$, let the point $$R2$$ divides PQ internally in the ratio $$2$$: $$1$$. Then, ⇒ $$R2=2$$×$$10+1$$×$$42+1$$,$$2$$×$$($$−$$16)+1$$×$$22+1$$,$$2$$×$$6+1$$×$$($$−$$6)1+2=20+43$$,−$$32+23$$,$$12$$−$$63=243$$,−$$303$$,$$63=(8$$,−$$10$$,$$2)Hence$$, required points are (6$$,$$-4$$, $$-$$ $$2) and (8$$, $$-$$ $$10$$,$$2).

Find the coordinates of the points which trisect the line segment joining the points P(4,2, - 6) and Q(10, - 16,6).

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