NCERT Class 12 · Ch 4 Exercise 4.2 · Q3
NCERT Class 12 Maths · Chapter 4 Determinants · Exercise 4.2 Question 3
Find k if the triangle area is 4 square units: (i) (k,0),(4,0),(0,2); (ii) (−2,0),(0,4),(0,k).
💡 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: (i) k=0 or 8; (ii) k=0 or 8.
- (i) The base on the x-axis has length |4−k| and height 2, so area=|4−k|.
- Set |4−k|=4: 4−k=4 or −4, hence k=0 or 8.
- (ii) The vertical base has length |k−4| and horizontal height 2, giving area=|k−4|.
- Set |k−4|=4: k−4=4 or −4, hence k=8 or 0.
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