The point of intersection of the lines x-6 -6 - y-4 4 - z-4 -8 and x-1 2 - y-2 4 - z-3 -2 is

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Angle between Two Lines

The point of ...

Question

The point of intersection of the lines $\frac{x - 6}{- 6} = \frac{y + 4}{4} = \frac{z - 4}{- 8}$ and $\frac{x + 1}{2} = \frac{y + 2}{4} = \frac{z + 3}{- 2}$ is

(0, 0, - 4)

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(1, 0, 0)

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(0, 2, 0)

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(1, 2, 0)

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Solution

The correct option is A $(0, 0, - 4)$
A point on the first line can be written as $(- 6 t + 6, 4 t - 4, - 8 t + 4)$ , while that on the second can be written as $(2 s - 1, 4 s - 2, - 2 s - 3)$
Equating the two coordinates, we have
$- 6 t + 6 = 2 s - 1 . . . (1)$
$4 t - 4 = 4 s - 2 . . . (2)$
Multiplying equation (1) by 2 and subtracting that from equation (1), we have
$- 6 t + 6 - (8 t - 8) = 0$
$∴ - 14 t + 14 = 0$ or $t = 1$
The point of intersection is therefore $(- 6 + 6, 4 - 4, - 8 + 4) = (0, 0, - 4)$

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The point of intersection of the lines x−6−6=y+44=z−4−8 and x+12=y+24=z+3−2 is

The point of intersection of the lines $\frac{x - 6}{- 6} = \frac{y + 4}{4} = \frac{z - 4}{- 8}$ and $\frac{x + 1}{2} = \frac{y + 2}{4} = \frac{z + 3}{- 2}$ is