NCERT Class 12 · Ch 10 Exercise 10.3 · Q15
NCERT Class 12 Maths · Chapter 10 Vector Algebra · Exercise 10.3 Question 15
Find ∠ABC for A(1,2,3), B(−1,0,0), C(0,1,2).
💡 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: ∠ABC=\(\operatorname{acos}{\left(\frac{5 \sqrt{102}}{51} \right)}\)
- At vertex B use BA=\(\left[\begin{matrix}2\\2\\3\end{matrix}\right]\) and BC=\(\left[\begin{matrix}1\\1\\2\end{matrix}\right]\).
- Their dot product is \(10\), and magnitudes \(\sqrt{17}\), \(\sqrt{6}\).
- Thus cos B=\(\frac{5 \sqrt{102}}{51}\) and B=\(\operatorname{acos}{\left(\frac{5 \sqrt{102}}{51} \right)}\).
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