Question Number 114443 by ARVIND990 last updated on 19/Sep/20

Commented byARVIND990 last updated on 19/Sep/20

fine the projection of point OP^(→) =p^→  in the  line r^→ =a^→ +λb^→

Answered by mr W last updated on 19/Sep/20

AP^(→) =p−a  say AN^(→) =βb  β∣b∣=AP^(→) ∙b  ⇒β=(((p−a)∙b)/(∣b∣))  ON^(→) =OA^(→) +AN^(→) =a+(((p−a)∙b)/(∣b∣))b  PN^(→) =a+(((p−a)∙b)/(∣b∣))b−p  OQ^(→) =OP^(→) +2PN^(→)   ⇒q=2a+((2(p−a)∙b)/(∣b∣))b−p

Commented byARVIND990 last updated on 19/Sep/20

i dont understand pls make a yours   digram and deep solution like how   AP=p−a pls

Commented byARVIND990 last updated on 19/Sep/20

and my question is projection of OP^(→)    and this is ∣OP^(→) ∣cosθ maybe

Commented byARVIND990 last updated on 19/Sep/20

∣OP^(→) ∣cosθ is equal to ((r^→ .p^→ )/(∣r^→ ∣)) =p^→ .r^�

Commented byARVIND990 last updated on 19/Sep/20

and pls show r^→  in daigram

Commented bymr W last updated on 19/Sep/20

OA^(→) +AP^(→) =OP^(→)   a+AP^(→) =p  ⇒AP^(→) =p−a

Commented bymr W last updated on 19/Sep/20

your question is about the projection  of point P  in line a+λb, that is the  point N, which is given by  ON^(→) =a+(((p−a)∙b)/(∣b∣))b  Q is the image of point P in the line  a+λb.

Commented bymr W last updated on 19/Sep/20

r=a+λb  (−∞<λ<+∞)  which is the line in your diagram  where the vector b is shown.

Commented bymr W last updated on 19/Sep/20