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Q17  Choose the correct answer. Let \vec a \: \: and \: \: \vec b  be two unit vectors and \theta  is the angle between them. Then \vec a + \vec bis a unit vector if

     \\A ) \theta = \frac{\pi }{4} \\\\ B ) \theta = \frac{\pi }{3} \\\\ C ) \theta = \frac{\pi }{2} \\\\ D ) \theta = \frac{2\pi }{3}

Answers (1)

best_answer

Gicen in the question

 \vec a \: \: and \: \: \vec b  be two unit vectors and \theta  is the angle between them

|\vec a|=1,\:and\:\:|\vec b|=1

also

|\vec a + \vec b|=1

|\vec a + \vec b|^2=1

|\vec a|^2 + |\vec b|^2+2\vec a.\vec b=1

1 + 1+2\vec a.\vec b=1

\vec a.\vec b=-\frac{1}{2}

|\vec a||\vec b|cos\theta =-\frac{1}{2}

cos\theta =-\frac{1}{2}

\theta =\frac{2\pi}{3}

Then \vec a + \vec b is a unit vector if \theta =\frac{2\pi}{3}

Hence option D is correct.

 

Posted by

Pankaj Sanodiya

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