Vector-let-L-1-AC-where-A-2-1-3-and-C-1-0-5-and-let-L-2-BD-where-B-1-3-0-and-D-3-4-1-Determine-the-distance-between-L-1-and-L-2-

Question Number 140690 by liberty last updated on 11/May/21

Vector

let L_{1} = AC where A = (2, - 1, 3) and

C = (1, 0, - 5) and let L_{2} = BD where

B = (1, 3, 0) and D = (3, - 4, 1) . Determine

the distance between L_{1} and L_{2} .

Answered by EDWIN88 last updated on 11/May/21

a vector that is simultaneously perpendicular

to L_{1} and L_{2} is N = \vec{A C} \times \vec{B D} = | \begin{matrix} - 1 1 - 8 \\ 2 - 7 1 \end{matrix} |

N = - 55 i - 15 j + 5 k

Then d = ∣ {pr}_{N} \vec{A B} ∣ = ∣ \vec{A B} . \frac{N}{∣ N ∣} ∣

d = \frac{∣ (- i + 4 j - 3 k) . 5 (- 11 i - 3 j + k) ∣}{5 \sqrt{121 + 9 + 1}}

d = \frac{∣ 11 - 12 - 3 ∣}{\sqrt{131}} = \frac{4}{\sqrt{131}}

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