NCERT Class 12 · Ch 4 Exercise 4.2 · Q2
NCERT Class 12 Maths · Chapter 4 Determinants · Exercise 4.2 Question 2
Show that (a,b+c), (b,c+a), (c,a+b) are collinear.
💡 Concept Hints
- Identify whether this needs determinant expansion, an inverse, or the absolute determinant formula for area.
- For a determinant use signed cofactors. For a system first check invertibility; for an area take half the absolute determinant.
✅ Step-by-Step Solution
Final Answer: The three points are collinear.
- Each point satisfies x+y=a+b+c, so all lie on the same straight line.
- Equivalently, in the area determinant C₁+C₂=(a+b+c)C₃. The columns are dependent, so the determinant and triangle area are zero.
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