JEE Advanced 2020 Paper 2 Mathematics Q11

Mathematics

Problem

Let a and b be positive real numbers. Suppose PQ⃗\vec{Q} = aî + bĵ and PS⃗\vec{S} = aî − bĵ are adjacent sides of a parallelogram PQRS. Let u⃗\vec{u} and v⃗\vec{v} be the projection vectors of w⃗\vec{w} = î + ĵ along PQ⃗\vec{Q} and PS⃗\vec{S}, respectively. If |u⃗\vec{u}| + |v⃗\vec{v}| = |w⃗\vec{w}| and if the area of the parallelogram PQRS is 8, then which of the following statements is/are TRUE?

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