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QJEEM24Ma2d3f: JEE Main 2024 Mathematics - Class 12 JEEM24Ma2d3f Solution: Let be the origin and the position vectors of and be and…

Let OO be the origin and the position vectors of AA and BB be 2i^+2j^+k^2 \hat{i}+2 \hat{j}+\hat{k} and 2i^+4j^+4k^2 \hat{i}+4 \hat{j}+4 \hat{k} respectively. If the internal bisector of ∠AOB\angle \mathrm{AOB} meets the line AB\mathrm{AB} at C\mathrm{C} , then the length of OCO C is

Multiple Choice Options

  • A 3234\frac{3}{2} \sqrt{34}
  • B 2331\frac{2}{3} \sqrt{31}
  • C 2334\frac{2}{3} \sqrt{34}
  • D 3231\frac{3}{2} \sqrt{31}

Step-by-Step Verified Solution

JEE Main 2024 (Online) 29th January Morning Shift Mathematics - 3D Geometry Question 44 English Explanation

 length of OC=1363=2343\text { length of } O C=\frac{\sqrt{136}}{3}=\frac{2 \sqrt{34}}{3}

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