If A \left(\right. 1 , - 2 , - 1 \left.\right) , B \left(\right. 4 , 0 , - 3 \left.\right) , C \left(\right. 1 , 2 , - 1 \left.\right) , D \left(\right. 2 , - 4 , - 5 \left.\right), find the distance between A B and C D.

Engineering

Mathematics

Line of Greatest Slope

Question

A (1, - 2, - 1), B (4, 0, - 3), C (1, 2, - 1), D (2, - 4, - 5)

, find the distance between

A B

and

C D

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Equation of

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

\vec{C D} = \frac{x - 1}{1} = \frac{y - 2}{- 6} = \frac{z + 1}{- 4}

Distance between them is given by

∣ \begin{array}{ccc} x_{1} - x_{2} & a m p; y_{1} - y_{2} & a m p; z_{1} - z_{2} \\ l_{1} & a m p; m_{1} & a m p; n_{1} \\ l_{2} & a m p; m_{2} & a m p; n_{2} \end{array} ∣

= ∣ \begin{array}{ccc} 0 & a m p; 4 & a m p; 0 \\ 3 & a m p; 2 & a m p; - 2 \\ 1 & a m p; - 6 & a m p; - 4 \end{array} ∣

= (- 4) (- 12 + 2) = 40

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