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MathsJEE Main 28 Jan 2026, Shift 2·Q17·MCQ·Tough

Vectors · Angle bisector and triangle area

Let PP be a point in the plane of the vectors AB→=3i^+j^−k^\overrightarrow{AB} = 3\hat i + \hat j - \hat k and AC→=i^−j^+3k^\overrightarrow{AC} = \hat i - \hat j + 3\hat k such that PP is equidistant from the lines ABAB and ACAC. If ∣AP→∣=52\left\lvert\overrightarrow{AP}\right\rvert = \dfrac{\sqrt5}{2}, then the area of the triangle ABPABP is :
  1. (1)2
  2. (2)32\dfrac32
  3. (3)304\dfrac{\sqrt{30}}{4}
  4. (4)264\dfrac{\sqrt{26}}{4}
We corrected a printing error in the original paper

Source printed “in the plane of the vector” (two vectors follow).

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