Let P be a point in the plane of the vectors AB=3i+j-k and AC=i-j… | JEE Main 2026 Mathematics PYQ

MCQMediumJEE Main 2026 · 28 January, Shift 2Equation of Line in 3D

Let $P$ be a point in the plane of the vectors $\vec{AB}=3\hat{i}+\hat{j}-\hat{k} \quad \text{and} \quad \vec{AC}=\hat{i}-\hat{j}+3\hat{k}$ such that $P$ is equidistant from the lines $AB$ and $AC$ . If $|\vec{AP}|=\frac{\sqrt5}{2}$ , then the area of triangle $ABP$ is:

A
$2$
B
$\frac{3}{2}$
C
$\frac{\sqrt{26}}{4}$
D
$\frac{\sqrt{30}}{4}$

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