Let us define the length of a vector $a\hat i +b\hat j+c\hat k$ as $|a|+|b|+|c|$. This definition coincides with the usual definition of length of a vector $a\hat i +b\hat j+c\hat k$ iff
Answer & explanation
Correct answer: option 2
We have,
$|a\hat i +b\hat j + c\hat k|=|a|+|b|+|c|$
$⇒\sqrt{a^2+b^2+c^2}=|a|+|b|+|c|$
$⇒a^2+b^2+c^2=a^2+b^2+c^2+2(|a||b|+|b||c|+|c||a|)$
$⇒|a||b|+|b||c|+|c||a|=0$
$⇒ab=bc = ca=0$
⇒ Any two of a, b, c are zero.