question_answer

If \[a.b=0\]and \[a+b\]makes an angle of \[{{30}^{o}}\] with a, then

A)  \[|b|=2|a|\]                       

B)         \[|a|=2|b|\]                       

C)        \[|a|=\sqrt{3}|b|\]             

D)         None of these

Correct Answer: C

Solution :

We have, \[a.b=0\Rightarrow a\bot b\] So, vectors a, b and \[a+b\]form a right angled triangle.                 In \[\Delta PQR,\]we have                                 \[\tan {{30}^{o}}=\frac{|b|}{|a|}\]                 \[\Rightarrow \]    \[|a|=\sqrt{3}|b|\]