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 point \left(\right. 1 , 3 , 5 \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 point

(1, 3, 5)

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Q (3 λ - 2, 2 λ - 1, 2 λ + 3)

Let

P (1, 3, 3)

be
the point

P Q = 5

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

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