The distance of the point (1, – 5, 9) from the plane x – y + z = 5 measured along the line x = y = z is

Engineering

Mathematics

Equation of Straight Line in 3D

Question

$\frac{20}{3}$

$3 \sqrt{10}$

$10 \sqrt{3}$

$\frac{10}{\sqrt{3}}$

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Equation of straight line parallel to x = y = z and passing through (1, –5, 9) is

$\frac{x - 1}{1} = \frac{y + 5}{1} = \frac{z - 9}{1} = r$

x = r + 1, y = r – 5, z = r + 9

x – y + z = 5

r + 1 – (r – 5) + r + 9 = 5

r = – 10.

B $\equiv$ (– 9, – 15, – 1)

$∴ AB = \sqrt{100 + 100 + 100} = 10 \sqrt{3} .$