Verified Solution • 2025–26 Session moderate

QJEEM12Ma07eb: JEE Main 2012 Physics - Class 11 JEEM12Ma07eb Solution: Let and be two unit vectors. If the vectors and are…

Let a→\overrightarrow a and b→\overrightarrow b be two unit vectors. If the vectors  c→=a^+2b^\,\overrightarrow c = \widehat a + 2\widehat b and d→=5a^−4b^\overrightarrow d = 5\widehat a - 4\widehat b are perpendicular to each other, then the angle between a→\overrightarrow a and b→\overrightarrow b is :

Multiple Choice Options

  • A π6{\pi \over 6}
  • B π2{\pi \over 2}
  • C π3{\pi \over 3}
  • D π4{\pi \over 4}

Step-by-Step Verified Solution

Let c→=a^+2b^\overrightarrow c = \widehat a + 2\widehat b and d→=5a^−4b^\overrightarrow d = 5\widehat a - 4\widehat b

Since c→\overrightarrow c and d→\overrightarrow d are perpendicular to each other

∴\therefore c→.d→=0⇒(a^+2b^).(5a^−4b^)=0\overrightarrow c .\overrightarrow d = 0 \Rightarrow \left( {\widehat a + 2\widehat b} \right).\left( {5\widehat a - 4\widehat b} \right) = 0

⇒5+6a^.b^−8=0\Rightarrow 5 + 6\widehat a.\widehat b - 8 = 0       \,\,\,\,\,\, (as a^.a^=1\widehat a.\widehat a = 1 )

⇒a^.b^=12⇒θ=π3\Rightarrow \widehat a.\widehat b = {1 \over 2} \Rightarrow \theta = {\pi \over 3}

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