NCERT Class 12 · Ch 10 Miscellaneous Exercise · Q6
NCERT Class 12 Maths · Chapter 10 Vector Algebra · Miscellaneous Exercise Question 6
Find a magnitude-5 vector parallel to the resultant of a=2i+3j−k and b=i−2j+k.
💡 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: ±\(\left[\begin{matrix}\frac{3 \sqrt{10}}{2}\\\frac{\sqrt{10}}{2}\\0\end{matrix}\right]\)
- The direction vector is \(\left[\begin{matrix}3\\1\\0\end{matrix}\right]\), with magnitude √(10)=\(\sqrt{10}\).
- Divide by this nonzero magnitude and multiply by 5: \(\left[\begin{matrix}\frac{3 \sqrt{10}}{2}\\\frac{\sqrt{10}}{2}\\0\end{matrix}\right]\). Either sign is parallel; the displayed positive sign has the same direction.
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