The length of foot of the perpendicular from the point $(2, - 1, 5)$ to the line $\frac{x - 11}{10} = \frac{y + 2}{- 4} = \frac{z + 8}{- 11}$ are ?

\sqrt{14}, (1, 2, - 3)

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\sqrt{14}, (1, - 2, 3)

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\sqrt{14}, (1, 2, 3)

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Solution

The correct option is C $\sqrt{14}, (1, 2, 3)$
$\begin{matrix} \frac{x - 11}{10} = \frac{y + 2}{- 4} = \frac{z + 8}{- 11} = t x = 10 t + 11, y = (- 4 t - 2), z = - 11 t - 8 B : (10 t + 11, - 4 t - 2, - 11 t - 8) A B : (10 t + 11 - 2, - 4 t - 2 + 1, - 11 t - 8 - 5) (10 t + 9, - 4 t - 1, - 11 t - 13) 10. (10 t + 9) - 4 (- 4 t - 1) - 11 (- 11 t - 13) = 0 100 t + 90 + 16 t + 4 + 121 t + 143 = 0 237 t = - 237 t = - 1 B; (1, 2, 3) A B = \sqrt{1 + 9 + 4} = \sqrt{14} u n i t . O p t i o n C i s c o r r e c t a n s w e r . \end{matrix}$

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Similar questions

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(2, - 1, 5)

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\frac{x - 14}{10} = \frac{y + 2}{- 4} = \frac{z + 8}{- 11}

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The length of foot of the perpendicular from the point (2, −1, 5) to the line x−1110=y+2−4=z+8−11 are ?

The length of foot of the perpendicular from the point $(2, - 1, 5)$ to the line $\frac{x - 11}{10} = \frac{y + 2}{- 4} = \frac{z + 8}{- 11}$ are ?