Show that the points A, B, C with position vectors 2i^–j^+k^,i^–3j^–5k^and3i^–4j^–4k^ respectively, are the vertices of a right-angled triangle. Hence find the area of the triangle.

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Show that the points A, B, C with position vectors {2}{{i}}–{{

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Show that the points A, B, C with position vectors $2 \hat{i} - \hat{j} + \hat{k}, \hat{i} - 3 \hat{j} - 5 \hat{k} and 3 \hat{i} - 4 \hat{j} - 4 \hat{k}$ respectively, are the vertices of a right-angled triangle. Hence find the area of the triangle.

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Show that the points A, B, C with position vectors

2 \hat{i} - \hat{j} + \hat{k}, \hat{i} - 3 \hat{j} - 5 \hat{k} and 3 \hat{i} - 4 \hat{j} - 4 \hat{k}

respectively, are the vertices of a right-angled triangle. Hence find the area of the triangle.

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Question Text

Show that the points A, B, C with position vectors

2 \hat{i} - \hat{j} + \hat{k}, \hat{i} - 3 \hat{j} - 5 \hat{k} and 3 \hat{i} - 4 \hat{j} - 4 \hat{k}

respectively, are the vertices of a right-angled triangle. Hence find the area of the triangle.