NCERT Class 12 · Ch 10 Exercise 10.4 · Q9
NCERT Class 12 Maths · Chapter 10 Vector Algebra · Exercise 10.4 Question 9
Find the area of triangle A(1,1,2), B(2,3,5), C(1,5,5).
💡 Concept Hints
- Write the vector components and identify the required direction or geometric relation.
- Use the magnitude, dot-product, cross-product or section formula that matches the requested quantity.
✅ Step-by-Step Solution
Final Answer: \(\frac{\sqrt{61}}{2}\) square units.
- Form AB=\(\left[\begin{matrix}1\\2\\3\end{matrix}\right]\) and AC=\(\left[\begin{matrix}0\\4\\3\end{matrix}\right]\).
- Compute AB×AC=\(\left[\begin{matrix}-6\\-3\\4\end{matrix}\right]\), with magnitude \(\sqrt{61}\).
- Triangle area is half the cross-product magnitude: \(\frac{\sqrt{61}}{2}\).
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