# If the magnitude of the vector $a\hat i+b\hat j+c\hat k$ is $|a|+|b|+|c|$, then $a,b,c$ should be ?

Given: $\sqrt {a^2+b^2+c^2}=|a|+|b|+|c|$
$\Rightarrow\:a^2+b^2+c^2=a^2+b^2+c^2+2(|a||b|+|b||c|+|c||a|)$
$\Rightarrow\:|a||b|+|b||c|+|c||a|=0$
This is possible iff $ab=bc=ac=0$
$i.e.,$ if any two of $a,b,c$ are zero.