The foot of the perpendicular $$fromP5$$,$$7$$,$$3$$ to the line which is passing through the points $$A12$$,$$21$$,$$10$$,$$B9$$,$$13$$,$$15$$ is

Question

The foot of the perpendicular $$fromP5$$,$$7$$,$$3$$  to the line which is passing through the points $$A12$$,$$21$$,$$10$$,$$B9$$,$$13$$,$$15$$ is

Infinity Learn · Accepted Answer

The equation of the line passing through the $$pointsA12$$,$$21$$,$$10$$  $$andB9$$,$$13$$,$$15$$  is   x−$$123=y$$−$$218=z$$−$$10$$−$$5$$           General point on the line $$isQ3k+12$$,$$8k+21$$,−$$5k+10Suppose$$ that Qbe the foot of the perpendicular to the $$P5$$,$$7$$,$$3point$$   on the above linePQ¯Hence, the line  is perpendicular to the above lineIt implies that             $$3k+7$$⋅$$3+8k+14$$⋅$$8+$$−$$5k+7$$⋅−$$5=09k+21+64k+112+25k$$−$$35=098k+98=0k=$$−$$1Therefore$$, the foot of the perpendicular is   $$Q9$$,$$13$$,$$15$$

The foot of the perpendicular from $P (5, 7, 3)$ to the line which is passing through the points $A (12, 21, 10)$ , $B (9, 13, 15)$ is

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The foot of the perpendicular fromP5,7,3 to the line which is passing through the points A12,21,10,B9,13,15 is

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The foot of the perpendicular from $P (5, 7, 3)$ to the line which is passing through the points $A (12, 21, 10)$ , $B (9, 13, 15)$ is