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JEE Advanced Mathematics question

MathematicsSolution of TrianglesJEE Advanced

Not in JEE syllabus

The position vectors of the vertices A, B, C of a triangle are , and respectively. The length of the bisector AD of the angle BAC where D is on the line segment BC, is

Answer: (D)

Solution

=(2Missing argument for \hat\hat i+Missing argument for \hat\hat j-2Missing argument for \hat\hat k)-(Missing argument for \hat\hat i-Missing argument for \hat\hat j-3Missing argument for \hat\hat k)=Missing argument for \hat\hat i+2Missing argument for \hat\hat j+Missing argument for \hat\hat k, ||=Missing argument for \sqrt\sqrt6,

=(-5Missing argument for \hat\hat i+2Missing argument for \hat\hat j-6Missing argument for \hat\hat k)-(Missing argument for \hat\hat i-Missing argument for \hat\hat j-3Missing argument for \hat\hat k)=-6Missing argument for \hat\hat i+3Missing argument for \hat\hat j-3Missing argument for \hat\hat k, ||==3Missing argument for \sqrt\sqrt6 .

By the angle-bisector theorem, D divides BC in the

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Question ID VK-109691