The perpendicular bisector of the line segment with end $$points2$$,$$3$$,$$2$$ and −$$4$$,$$1$$,$$4$$ passes through the point −$$3$$,$$6$$,$$1and$$ has equation of the form $$x+3a=y$$−$$6b=z$$−$$1cwhere$$ a,b,c are relatively prime integers with a$$0$$ , then the value of abc−$$a+b+c$$ is

Question

The perpendicular bisector of the line segment  with end $$points2$$,$$3$$,$$2$$ and −$$4$$,$$1$$,$$4$$ passes through the point  −$$3$$,$$6$$,$$1and$$ has equation of the form $$x+3a=y$$−$$6b=z$$−$$1cwhere$$ a,b,c are relatively prime integers with a>$$0$$ , then the value of abc−$$a+b+c$$ is

Infinity Learn · Accepted Answer

The midpoint of the line segment joining $$2$$,$$3$$,$$2$$,−$$4$$,$$1$$,$$4is2$$−$$42$$,$$3+12$$,$$2+42=$$−$$1$$,$$2$$,$$3$$  Given that the perpendicular bisector is passing through the point −$$3$$,$$6$$,$$1$$ alsoHence the equation of the perpendicular bisector is  $$x+3$$−$$1+3=y$$−$$62$$−$$6=z$$−$$13$$−$$1Rewrite$$ the above equation as  $$x+3$$−$$1+3=y$$−$$62$$−$$6=z$$−$$13$$−$$1Comparing$$ this with the given $$linea=1$$,$$b=$$−$$2$$,$$c=1Consider$$ the expression abc−$$a+b+c=$$−$$2$$−$$0=$$−$$2$$

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

The perpendicular bisector of the line segment with end points2,3,2 and −4,1,4 passes through the point −3,6,1and has equation of the form x+3a=y−6b=z−1cwhere a,b,c are relatively prime integers with a>0 , then the value of abc−a+b+c is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material