NCERT Class 12 · Ch 10 Exercise 10.2 · Q17
NCERT Class 12 Maths · Chapter 10 Vector Algebra · Exercise 10.2 Question 17
Show the points with position vectors (3,−4,−4),(2,−1,1),(1,−3,−5) 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 A.
- The displacements are AB=\(\left[\begin{matrix}-1\\3\\5\end{matrix}\right]\), AC=\(\left[\begin{matrix}-2\\1\\-1\end{matrix}\right]\), BC=\(\left[\begin{matrix}-1\\-2\\-6\end{matrix}\right]\).
- Squared side lengths are \(35\), \(6\), \(41\). The largest equals the sum of the other two.
- The adjacent-side dot products at A,B,C are \(0\), \(35\), \(6\), respectively; zero identifies the right angle at A.
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