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The area of the square, one of whose diagonals is 3î + 4ĵ is

The area of the square, one of whose diagonals is 3î + 4ĵ is Correct Answer 12.5 square unit

Concept:

1. Let, p̅  = xi + yj, then, Magnitude of p = |p̅| = √(x2 + y2)

2. Consider a square of side 'a'.

Area of square = a2

Diagonal of square = √2 a

 

Calculation:

Let, diagonal d̅  = 3î + 4ĵ 

∴ |d̅| = √(32 + 42) = √(9 + 16)

⇒ |d̅| = 5

But diagonal of square with side a, is √2 a

∴ 5 = √2 a

⇒ a  = 5/√2

Now,  area of square

 a2 = (5/√2)2

⇒ Area  = 25/2

= 12.5 sq units

 

Hence, option (2) is correct.

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