Question

a,b,c are mutually perpendicular unit vector, then find the value of [a,b,c]:

Answer 1

$\left[\hat{a}\hat{b}\hat{c}\right]$ perpendicular normal vectors to both $\hat{b}$ and $\hat{c}$ is $\hat{a}$

$=\hat{a}\cdot (\hat{b}\times \hat{c})$

$=\hat{a}\cdot (|\hat{b}||\hat{c}|\sin {90}^o\cdot \hat{a})$

$=\hat{a}\cdot \left(1\right(1\left)\right(1\left)\hat{a}\right)$

$=\hat{a}\cdot \hat{a}$

$=|\hat{a}{|}^2=1$

$\therefore \left[\hat{a}\hat{b}\hat{c}\right]=1$