NCERT Class 12 · Ch 10 Miscellaneous Exercise · Q13
NCERT Class 12 Maths · Chapter 10 Vector Algebra · Miscellaneous Exercise Question 13
The dot product of i+j+k with a unit vector along the sum (2,4,−5)+(λ,2,3) is 1. Find λ.
💡 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: λ=1.
- The resultant is (λ+2,6,−2), of norm √[(λ+2)²+40]. The equation is (λ+6)/√[(λ+2)²+40]=1.
- Squaring gives (λ+6)²=(λ+2)²+40, hence 8λ=8 and λ=1.
- Check the original sign: λ+6=7>0 and the norm is 7, so this candidate satisfies the unsquared equation.
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