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Two drones are being used for soil analysis over an area of farmland. Drone A has been programmed…

Mathematics20254 marksShort answer
Two drones are being used for soil analysis over an area of farmland. Drone A has been programmed to fly on the path given by $\vec{r} = 6\hat{i} + 2\hat{j} + 2\hat{k} + \lambda(\hat{i} - 2\hat{j} + 2\hat{k})$ and drone B has been programmed to fly on the path $\vec{r} = -4\hat{i} - \hat{k} + \mu(3\hat{i} - 2\hat{j} - 2\hat{k})$. At what points on their respective paths should they reach, so that they will be closest to each other?

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Three-dimensional Geometry

From ISC 2025 Practice Mathematics, question 123.