First slide

Straight lines in 3D

Question

If the lines $\frac{x - 2}{1} = \frac{y - 3}{1} = \frac{z - 4}{λ} and \frac{x - 1}{λ} = \frac{y - 4}{2} = \frac{z - 5}{1}$ intersect, then

Moderate

A

$λ = - 1$
B

$λ = 0$
C

$λ = - 3$
D

$λ = 0$

Solution

The given lines intersect if
$|\begin{array}{ccc} 2 - 1 & 3 - 4 & 4 - 5 \\ 1 & 1 & λ \\ λ & 2 & 1 \end{array}| = 0 \Rightarrow λ = 0, - 1$

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