Find the foot of the perpendicular drawn from the point to the line Also, find the length of the perpendicular.

Question

Philoid · Accepted Answer

Given: - Point with position vector and equation of line

Let, PQ be the perpendicular drawn from P () to given line whose endpoint/ foot is Q point.

Q is on line

⇒ is the position vector of Q

Hence,

⇒

Since, PQ is perpendicular on line

Therefore, their Dot product is zero

Compare given line equation with

⇒

⇒ 14λ – 14 = 0

⇒ λ = 1

Hence Position vector of Q by putting the value of λ

⇒

⇒ ; Foot of perpendicular

and Distance PQ, putting the value of λ in PQ vector equation, we get

⇒

Now, Magnitude of PQ

We know that,

; where x,y,z are coefficient of vector

Hence

⇒

⇒ units