NCERT Class 12 · Ch 10 Miscellaneous Exercise · Q7
NCERT Class 12 Maths · Chapter 10 Vector Algebra · Miscellaneous Exercise Question 7
For a=i+j+k, b=2i−j+3k, c=i−2j+k, find a unit vector parallel to 2a−b+3c.
💡 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: ±\(\left[\begin{matrix}\frac{3 \sqrt{22}}{22}\\- \frac{3 \sqrt{22}}{22}\\\frac{\sqrt{22}}{11}\end{matrix}\right]\)
- The direction vector is \(\left[\begin{matrix}3\\-3\\2\end{matrix}\right]\), with magnitude √(22)=\(\sqrt{22}\).
- Divide by this nonzero magnitude: \(\left[\begin{matrix}\frac{3 \sqrt{22}}{22}\\- \frac{3 \sqrt{22}}{22}\\\frac{\sqrt{22}}{11}\end{matrix}\right]\). Either sign is parallel; the displayed positive sign has the same direction.
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