The point of intersection of the lines x - 1 2 = y - 2 3 = z - 3 4 and x - 4 5 = y - 1 2 = z , is:

Question

The point of intersection of the lines $\frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4}$ and $\frac{x - 4}{5} = \frac{y - 1}{2} = z,$ is:

Smart Achievers · Accepted Answer

(4)

Ans. $(- 1, - 1, - 1)$

Explanation:

$\frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4} = λ$

$\Rightarrow$ $x = 2 λ + 1, y = 3 λ + 2, z = 4 λ + 3$

Also, $\frac{x - 4}{5} = \frac{y - 1}{2} = \frac{z}{1} = μ$

$\Rightarrow$ $x = 5 μ + 4, y = 2 μ + 1, z = μ$

Now, $2 λ + 1 = 5 μ + 4$

$3 λ + 2 = 2 μ + 1$

$4 λ + 3 = μ$

On solving, $λ = - 1, μ = - 1$

$x = - 1, y = - 1, z = - 1$

$∴$ $Point = (- 1, - 1, - 1)$

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