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Consider a \(\triangle ABC\) where \(A (1,3,2), B (-2,8,0)\) and \(C (3,6,7)\). If the angle bisector of \(\angle BAC\) …

Q1
PYQ

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

[JEE Main 2024, 01 Feb (Shift 2)]

a

\(\sqrt{19}\)

b

\(\frac{39}{2 \sqrt{38}}\)

c

\(\frac{37}{2 \sqrt{38}}\)

d

\(\frac{\sqrt{38}}{2}\)

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