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JEE Advanced 2026 Mathematics question

MathematicsVector AlgebraJEE Advanced 2026

Let be two vectors, and let , and be the points with position vectors , and , respectively, with respect to the origin . If , , and and are perpendicular to each other, then the area of the triangle is

Answer: (C)

Solution

Perpendicularity gives , i.e. . From the two length conditions,

|Missing argument for \vec\vec a+Missing argument for \vec\vec b|^2=|Missing argument for \vec\vec a|^2+2 Missing argument for \vec\vec a·Missing argument for \vec\vec b+|Missing argument for \vec\vec b|^2=21, |Missing argument for \vec\vec a-Missing argument for \vec\vec b|^2=|Missing argument for \vec\vec a|^2-2 Missing argument for \vec\vec a·Missing argument for \vec\vec b+|Missing argument for \vec\vec b|^2=9 .

Subtracting, \vec\vec\vec$

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Question ID VK-104753