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QJEEM24Ma9111: JEE Main 2024 Mathematics - Class 12 JEEM24Ma9111 Solution: Consider a where and . If the angle bisector of meets the line…

Consider a △ABC\triangle A B C where A(1,3,2),B(−2,8,0)A(1,3,2), B(-2,8,0) and C(3,6,7)C(3,6,7) . If the angle bisector of ∠BAC\angle B A C meets the line BCB C at DD , then the length of the projection of the vector AD→\overrightarrow{A D} on the vector AC→\overrightarrow{A C} is :

Multiple Choice Options

  • A 37238\frac{37}{2 \sqrt{38}}
  • B 19\sqrt{19}
  • C 39238\frac{39}{2 \sqrt{38}}
  • D 382\frac{\sqrt{38}}{2}

Step-by-Step Verified Solution

JEE Main 2024 (Online) 1st February Evening Shift Mathematics - 3D Geometry Question 59 English Explanation

DD divides BCB C in ratio 1:11: 1

D:(12,7,72)

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Projection of AD→\overrightarrow{A D} on AC→\overrightarrow{A C}

=−1+12+1524+9+25=37238

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