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

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