NCERT Class 12 · Ch 10 Exercise 10.2 · Q8
NCERT Class 12 Maths · Chapter 10 Vector Algebra · Exercise 10.2 Question 8
Find a unit vector in direction PQ for P(1,2,3), Q(4,5,6).
💡 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: \(\left[\begin{matrix}\frac{\sqrt{3}}{3}\\\frac{\sqrt{3}}{3}\\\frac{\sqrt{3}}{3}\end{matrix}\right]\)
- The direction vector is \(\left[\begin{matrix}3\\3\\3\end{matrix}\right]\), with magnitude √(27)=\(3 \sqrt{3}\).
- Divide by this nonzero magnitude: \(\left[\begin{matrix}\frac{\sqrt{3}}{3}\\\frac{\sqrt{3}}{3}\\\frac{\sqrt{3}}{3}\end{matrix}\right]\).
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