Area of Triangle ABP (Jee Mains)

Vector Algebra and Components

Medium

Area of Triangle ABP

Let P be a point in the plane of the vector $\overrightarrow {AB} = 3\hat i + \hat j - \hat k$ and $\overrightarrow {AC} = \hat i - \hat j + 3\hat k$ such that P is equidistant from the lines AB and AC. If $\left| {\overrightarrow {AP} } \right| = \frac{{\sqrt 5 }}{2}$ , then the area of the triangle ABP is :

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