Mathematics

Mathematics

Problem

Three robotic ants are moving on a 2D plane. Their paths form a △with\triangle with vertices defined by position vectors r⃗1=3i^\vec{r}_{1} = 3\hat{i}, r⃗2=4j^\vec{r}_{2} = 4\hat{j}, and r⃗3=−2i^−j^\vec{r}_{3} = -2\hat{i} - \hat{j} relative to an origin. Using the property that the dot product of a side vector and its corresponding altitude vector is zero, find the coordinates of the orthocenter.

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