NCERT Class 12 · Ch 10 Exercise 10.2 · Q10
NCERT Class 12 Maths · Chapter 10 Vector Algebra · Exercise 10.2 Question 10
Find a vector in direction 5i−j+2k with magnitude 8.
💡 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: \(\left[\begin{matrix}\frac{4 \sqrt{30}}{3}\\- \frac{4 \sqrt{30}}{15}\\\frac{8 \sqrt{30}}{15}\end{matrix}\right]\)
- The direction vector is \(\left[\begin{matrix}5\\-1\\2\end{matrix}\right]\), with magnitude √(30)=\(\sqrt{30}\).
- Divide by this nonzero magnitude and multiply by 8: \(\left[\begin{matrix}\frac{4 \sqrt{30}}{3}\\- \frac{4 \sqrt{30}}{15}\\\frac{8 \sqrt{30}}{15}\end{matrix}\right]\).
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