If the projection of point p p¯ on the plane r¯.n¯ = q is the point S(s¯) then

s¯−p¯=λn¯ and s¯⋅n¯=qs¯=p¯+λn¯:s¯⋅n¯=q(p¯+λn¯)⋅n¯=qp¯n¯+λλ∣¯2=qλ|n¯|2=q−p¯⋅n¯s¯=p¯+(q−p¯⋅n¯)n¯|n¯|2

If the projection of point p p¯ on the plane r¯.n¯ = q is the point S(s¯) then

s¯−p¯=λn¯ and s¯⋅n¯=qs¯=p¯+λn¯:s¯⋅n¯=q(p¯+λn¯)⋅n¯=qp¯n¯+λλ∣¯2=qλ|n¯|2=q−p¯⋅n¯s¯=p¯+(q−p¯⋅n¯)n¯|n¯|2

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

If the projection of point p $(\bar{p})$ on the plane $\bar{r} . \bar{n}$ = q is the point $S (\bar{s})$ then

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

$\bar{s} = \frac{(q - \bar{p} . \bar{n})}{{| \bar{n} |}^{2}} - \bar{p}$

$\bar{s} = \bar{p} + \frac{(q - \bar{p} . \bar{n}) \bar{n}}{{| \bar{n} |}^{2}}$

$\bar{s} = \bar{p} - \frac{(\bar{p} - \bar{n}) \bar{n}}{{| \bar{n} |}^{2}}$

$\bar{s} = \bar{p} - \frac{(\bar{q} - \bar{p} . \bar{n}) \bar{n}}{{| \bar{n} |}^{2}}$

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$\begin{array}{r} \bar{s} - \bar{p} = λ \bar{n} and \bar{s} \cdot \bar{n} = q \\ \bar{s} = \bar{p} + λ \bar{n} : \bar{s} \cdot \bar{n} = q \\ (\bar{p} + λ \bar{n}) \cdot \bar{n} = q \\ \bar{p} \bar{n} + {λ \bar{λ ∣}|}^{2} = q \\ λ | \bar{n} |^{2} = q - \bar{p} \cdot \bar{n} \\ \bar{s} = \bar{p} + \frac{(q - \bar{p} \cdot \bar{n}) \bar{n}}{| \bar{n} |^{2}} \end{array}$