Let a and b be positive real numbers. Suppose \overrightarrow{{PQ}}= {ai^{\^}}+ {bj^{\^}} and \overrightarrow{{PS}}= {ai^{\^}}- {bj^{\^}} are adjacent sides of aparallelogram PQRS. Let \overrightarrow{u} and \overrightarrow{{v}} be the projection vectors of \overrightarrow{{w}}= \stackrel{\^}{i}+ \stackrel{\^}{j} along \overrightarrow{{PQ}} and \overrightarrow{{PS}},respectively. If |\overrightarrow{{u}}|+|\overrightarrow{{v}}|=|\overrightarrow{{w}}| and if the area of the parallelogram PQRS is 8, then which of the following statements is/are TRUE? [JEE Adv 2020 P2]

The length of the diagonal PR of the parallelogram PQRS is 4

w ^{\to} is an angle bisector of the vectors {PQ} ^{\to} and {PS} ^{\to}

Vector Algebra

Section: Mathematics

Question : 12 of 38

Marks: +1, -0

Let a and b be positive real numbers. Suppose

→

and

→

−b

are adjacent sides of aparallelogram PQRS. Let

→

and

→

be the projection vectors of

→

along

→

and

→

,respectively. If |

→

|+|

→

|=|

→

| and if the area of the parallelogram PQRS is 8, then which of the following statements is/are TRUE?

[JEE Adv 2020 P2]

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