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Vector Algebra question

2020 · Shift 2 · Q29

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PYQ Library
JEE Advanced
Mathematics
Vector Algebra
2020 · Shift 2 · Q29

Vector Algebra question

2020 · Shift 2 · Q29

JEE AdvancedMathematicsVector AlgebraMultiple correct+4 / −2

Let a and b be positive real numbers. Suppose

PQ = a\widehat i + b\widehat j

and

PS = a\widehat i - b\widehat j

are adjacent sides of a parallelogram PQRS. Let u and v be the projection vectors of

w = \widehat i + \widehat j

along PQ and PS, respectively. If |u| + |v| = |w| and if the area of the parallelogram PQRS is 8, then which of the following statements is/are TRUE?

A
a + b = 4
B
a $-$ b = 2
C
The length of the diagonal PR of the parallelogram PQRS is 4
D
w is an angle bisector of the vectors PQ and PS

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