InterviewSolution
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InterviewSolution
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Show that the points A, B and C having position vectors (i + 2j + 7k),(2i + 6j + 3k) and (3i + 10j - 3k) respectively, are collinear. |
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Answer» A = \(\vec{i}+2\vec{j}+7\vec{k}\) B = \(2\vec{i}+6\vec{j}+2\vec{k}\) C = \(3\vec{i}+10\vec{j}-3\vec{k}\) \(\vec{AB}\) = \((2\vec{i}+6\vec{j}+2\vec{k})\) - \((\vec{i}+2\vec{j}+7\vec{k})\) = \(\vec{i}+4\vec{j}-5\vec{k}\) \(\vec{BC}\) \((3\vec{i}+10\vec{j}-3\vec{k})\) - \((2\vec{i}+6\vec{j}+2\vec{k})\) = \(\vec{i}+4\vec{j}-5\vec{k}\) \(\vec{AB}\) = \(\vec{BC}\) So, the points A, B and C are collinear. |
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