NCERT Class 12 · Ch 10 Exercise 10.4 · Q2
NCERT Class 12 Maths · Chapter 10 Vector Algebra · Exercise 10.4 Question 2
Find a unit vector perpendicular to a+b and a−b, where a=(3,2,2), b=(1,2,−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: ±\(\left[\begin{matrix}\frac{2}{3}\\- \frac{2}{3}\\- \frac{1}{3}\end{matrix}\right]\)
- The direction vector is \(\left[\begin{matrix}16\\-16\\-8\end{matrix}\right]\), with magnitude √(576)=\(24\).
- Divide by this nonzero magnitude: \(\left[\begin{matrix}\frac{2}{3}\\- \frac{2}{3}\\- \frac{1}{3}\end{matrix}\right]\). Either sign is parallel; the displayed positive sign has the same direction.
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