Question

Let us define the length of 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 $a\hat{i}+b\hat{j}+c\hat{k}$ if and only if

• A. $a=b=c=0$
• B. Any two of $a,b$ and $c$ are zero
• C. Any one of $a,b$ and $c$ is zero
• D. $a+b+c=0$

Answer 1

The correct option is B Any two of $a,b$ and $c$ are zero

$|a|+|b|+|c|=\sqrt{a^2+b^2+c^2}$
On squaring, we get
$\Rightarrow 2|ab|+2|bc|+2|ca|=0$
$\Rightarrow |a||b|=|b||c|=|c||a|=0$
Hence, any two of $a,b$ and $c$ are zero.
Hence, option '$B$' is correct.