find the point in whoch the line joining the points (-9,4,5) and (11,0,-1) is met by perpendicular from the origin - Maths - Introduction to Three Dimensional Geometry

Question

find the point in whoch the line joining the points (-9,4,5) and
(11,0,-1) is met by perpendicular from the origin

Neha Sethi · Accepted Answer

Dear student
Equations of the line joining the points -9,4,5 and (11,0,-1)in symmetrical form arex+911+9=y-40-4=z-5-1-5⇒x+920=y-4-4=z-5-6⇒x+910=y-4-2=z-5-3=r    (say)      
(1)Therefore, Any point on this line isP-9+10r,4-2r,5-3rLet P be the foot of the prependicular from the origin to line(1)
Then,D
R's of OP are-9+10r-0,4-2r-0,5-3r-0or, 10r-9,-2r+4,-3r+5∵OP is prependicular to line (1)∴1010r-9-2-2r+4-3-3r+5=0⇒100r-90+4r-8+9r-15=0⇒113r-113=0⇒r=1∴P1,2,2 which are the required co-ordinates
Regards

find the point in whoch the line joining the points (-9,4,5) and (11,0,-1) is met by perpendicular from the origin.