NCERT Class 12 · Ch 10 Exercise 10.3 · Q17
NCERT Class 12 Maths · Chapter 10 Vector Algebra · Exercise 10.3 Question 17
Show the points with position vectors (2,−1,1),(1,−3,−5),(3,−4,−4) form a right-angled triangle.
💡 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: Right-angled at C.
- The displacements are AB=\(\left[\begin{matrix}-1\\-2\\-6\end{matrix}\right]\), AC=\(\left[\begin{matrix}1\\-3\\-5\end{matrix}\right]\), BC=\(\left[\begin{matrix}2\\-1\\1\end{matrix}\right]\).
- Squared side lengths are \(41\), \(35\), \(6\). The largest equals the sum of the other two.
- The adjacent-side dot products at A,B,C are \(35\), \(6\), \(0\), respectively; zero identifies the right angle at C.
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