The foot of the perpendicular from 0- 2-3 to the line x-3-5-y-1-2-z-4-3 is-

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Foot of Perpendicular of a Point on a Line

The foot of t...

Question

The foot of the perpendicular from (0, 2,3) to the line $\frac{x + 3}{5} = \frac{y - 1}{2} = \frac{z + 4}{3}$ is:

(–2, 3, 4)

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(2, –1, 3)

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(2, 3, –1)

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(3, 2, –1)

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Solution

The correct option is C (2, 3, –1)
Any point on the given line is (5r – 3, 2r + 1, 3r – 4). If it is the foot of the perpendicular from (0, 2, 3), then 5(5r – 3 – 0) + 2(2r + 1 – 2) + 3(3r – 4 – 3) = 0
i.e.,38r = 38
i.e., r = 1
Foot of perpendicular is (2, 3, –1)

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Similar questions

Q. The foot of the perpendicular from P(1, 0, 2) to the line

\frac{x + 1}{3} = \frac{y - 2}{- 2} = \frac{z + 1}{- 1}

Q. Find the coordinates of foot of the perpendicular drawn from the point

(2, 3, - 1)

to line

\frac{x - 3}{3} = \frac{y - 2}{1} = \frac{z}{2}

Q. Equation of the plane perpendicular to the line

\frac{x - 1}{3} = \frac{y - 5}{2} = \frac{z + 3}{- 4}

and passing through the point

(1, - 2, 3)

Q. The locus of foot of the perpendiculars drawn from the line

\frac{x - 2}{2} = \frac{y - 1}{1} = \frac{z}{3}

to the plane

x + y + z = 1

Find the foot of perpendicular from the point (2,3,-8) to $\frac{4 - x}{2} = \frac{y}{6} = \frac{1 - z}{3}$ . Also, find the perpendicular distance from the given point to the line.

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The foot of the perpendicular from (0, 2,3) to the line x+35=y−12=z+43 is:

The correct option is C (2, 3, –1)Any point on the given line is (5r – 3, 2r + 1, 3r – 4). If it is the foot of the perpendicular from (0, 2, 3), then 5(5r – 3 – 0) + 2(2r + 1 – 2) + 3(3r – 4 – 3) = 0 i.e.,38r = 38 i.e., r = 1 Foot of perpendicular is (2, 3, –1)

The foot of the perpendicular from (0, 2,3) to the line $\frac{x + 3}{5} = \frac{y - 1}{2} = \frac{z + 4}{3}$ is:

The correct option is C (2, 3, –1)
Any point on the given line is (5r – 3, 2r + 1, 3r – 4). If it is the foot of the perpendicular from (0, 2, 3), then 5(5r – 3 – 0) + 2(2r + 1 – 2) + 3(3r – 4 – 3) = 0
i.e.,38r = 38
i.e., r = 1
Foot of perpendicular is (2, 3, –1)