Find the coordinates of the point which divides the line segment joining the points $$(-$$ $$2$$, $$3$$, $$5)$$ and (1$$, $$-$$ $$4$$,$$6) in the ratio $$2$$ : $$3$$ externally.

Question

Infinity Learn · Accepted Answer

Let the point C divides the line externally in the ratio $$2$$:$$3$$.Here, the ratio is $$2$$ :$$3$$.$$m=2$$,$$n=3The$$ coordinates of point $$C=mx2$$−$$nx1m$$−n,$$my2$$−$$ny1m$$−n,$$mz2$$−$$nz1m$$−n⇒$$C=2$$×(1)−$$3$$×$$($$−$$2)(2$$−$$3)$$,$$2$$×$$($$−$$4)$$−$$3$$×$$3(2$$−$$3)$$,$$2$$×$$6$$−$$3$$×$$5(2$$−$$3)=2+6($$−$$1)$$,−$$8$$−$$9($$−$$1)$$,$$12$$−$$15($$−$$1)=($$−$$8$$,$$17$$,$$3)$$

Find the coordinates of the point which divides the line segment joining the points (- 2, 3, 5) and (1, - 4,6) in the ratio 2 : 3 externally.

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