Given, $A C =3 i -4 j - k$
and $B D =2 i +3 j -6 k$
Let sides of a rhombus be $a$ and $b$. In $\Delta A B C$
$A C = A B + B C$
$\Rightarrow 3 i -4 j - k = a + b \cdots(i)$
$B D = B A + A D$
$\Rightarrow 2 i +3 j -6 k =- a + b ... (ii)$
On adding Eqs. (i) and (ii), we get
$5 i - j -7 k =2 b$
$\Rightarrow |2 b |=\sqrt{5^{2}+1^{2}+7^{2}}$
$\Rightarrow | b |=\frac{\sqrt{25+1+49}}{2}$
$\Rightarrow | b |=\frac{\sqrt{75}}{2}=\frac{5 \sqrt{3}}{2}$
