Class 12 Vector Algebra · Long Answer3 Markscross_product_area
Class 12 Maths · Vector Algebra · Long Answer #73
Show A=(2,−1,1), B=(1,−3,−5), C=(3,−4,−4) form a right triangle and find its area.
✅ Step-by-Step Solution
Final Answer: Right angle at C; area=√210/2
- Compute CA=(−1,3,5) and CB=(−2,1,−1).
- CA·CB=2+3−5=0, so the right angle is at C. Their squared norms are 35 and 6.
- Area=½|CA||CB|=½√35√6.
- Thus the triangle is right-angled at C and has area √210/2 square units.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Compute CA=(−1,3,5) and CB=(−2,1,−1).
- [1 mark] CA·CB=2+3−5=0, so the right angle is at C. Their squared norms are 35 and 6.
- [1 mark] Area=½|CA||CB|=½√35√6.
- [0.5 marks] Thus the triangle is right-angled at C and has area √210/2 square units.
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