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 \left(\right. 1 , 3 , 3 \left.\right).

Engineering

Mathematics

Line of Greatest Slope

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

\to

General point on the

line would be

(3 λ - 2, 2 λ - 1, 2 λ + 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

\Rightarrow 17 λ^{2} + 25 - 34 λ, = 25

\Rightarrow 17 λ (λ - 2) = 0

\Rightarrow λ, = 0

λ = 2

\Rightarrow

Posible points :-

(- 2, - 1, 3), (4, 3, 7)

Please subscribe our Youtube channel to unlock this solution.