MCQ
The vector $a + b$ bisects the angle between the vectors $ a $ and $ b,$ if
- A$|a|\, = \,|b|$
- ✓$|a|\, = \,|b|$ or angle between a and b is zero
- C$|a|\,\, = m\,|b|$
- DNone of these
$\frac{{(a + b)\,.\,a}}{{|a + b|\,|a|}} = \frac{{(a + b)\,.\,b}}{{|a + b|\,|b|}}$
$ \Rightarrow \frac{{|a{|^2}}}{{|a + b|\,|a|}} + \frac{{b\,.\,a}}{{|a + b|\,|a|}} = \frac{{a\,.\,b}}{{|a + b|\,|b|}} + \frac{{|b{|^2}}}{{|a + b|\,|b|}}$
$ \Rightarrow \frac{{|a| - |b|}}{{|a + b|}}\left( {1 - \frac{{a\,.\,b}}{{|a|\,|b|}}} \right) = 0$
Hence $|a|\, = \,|b|$ or angle between $a$ and $b$ is $0$.
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