Verified Solution • 2025–26 Session moderate

QJEEM21Ma4401: JEE Main 2021 Physics - Class 11 JEEM21Ma4401 Solution: Let a vector be obtained by rotating the vector by an angle 45…

Let a vector αi^+βj^\alpha \widehat i + \beta \widehat j be obtained by rotating the vector 3i^+j^\sqrt 3 \widehat i + \widehat j by an angle 45 ∘^\circ about the origin in counterclockwise direction in the first quadrant. Then the area of triangle having vertices ( α\alpha , β\beta ), (0, β\beta ) and (0, 0) is equal to :

Multiple Choice Options

  • A 12{1 \over {\sqrt 2 }}
  • B 12{1 \over 2}
  • C 1
  • D 2 2{\sqrt 2 }

Step-by-Step Verified Solution

JEE Main 2021 (Online) 16th March Morning Shift Mathematics - Vector Algebra Question 159 English Explanation
( α\alpha , β\beta ) ≡\equiv (2 cos 75 ∘^\circ , 2 sin 75 ∘^\circ )

Area = 12{1 \over 2} (2 cos 75 ∘^\circ ) (2 sin 75 ∘^\circ )

= sin(150 ∘^\circ ) = 12{1 \over 2} square unit

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