Find the points on the line at a distance of 5 units from the points (1,3,3).

Engineering

Mathematics

Length of Perpendicular

Section Formulae and Centres of a Triangle

Equation of Straight Line in 3D and Distance Of a Point From Line

Question

Find the points on the line $\frac{x + 2}{3} = \frac{y + 1}{2} = \frac{z - 3}{2}$ at a distance of 5 units from the points (1,3,3).

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

→ General point on the line would be

(3λ −2,2λ −1,2λ +3)

it is at distance 5 units from (1,3,3)

$\to \sqrt{(3 λ - 3)^{2} + (2 λ - 4)^{2} + (2 λ)^{2}} = 5$

⇒ 17λ²+ 25 − 34λ =25

⇒ 17λ(λ − 2) = 0

⇒ λ = 0 or λ = 2