10. vector algebra — Maths STD 12 Science — Question

$ \Rightarrow \left| {|a||b|\sin \theta \,n.c} \right| = |a||b||c|$

$ \Rightarrow \left| {|a||b||c|\sin \theta \cos \alpha } \right| = |a||b||c|$

$ \Rightarrow {\rm{ }}|\sin \theta ||\cos \alpha | = 1 \Rightarrow \theta = \frac{\pi }{2}$ and $\alpha = 0$

$ \Rightarrow a \bot b$ and $c||n$

$ \Rightarrow a \bot b$ and $c$is perpendicular to both $a$and $b$

 $\therefore a,\,b,\,c$ are mutually perpendicular

Hence, $a.b = b.c = c.a = 0.$