Let `a=a_(1)hati+a_(3)hatk, b=b_(1)hati+b_(3)hatk, c=c_(1)hati+c_(2)hatj+c_(3)hatk`. If `|c|=1 and (axxb)xxc=0`, then `|(a_(1),a_(2),a_(2)),(b_(1),b_(2),b_(3)),(c_(1),c_(2),c_(3))|` is equal to

Options

A. 0
B. 1
C. `|a|^(2)|b|^(2)`
D. `|axxb|^(2)`

Answer

D

Explanation

Given, `(axxb)xxc=0, " then " c = (axxb)/(|axxb|) `
`therefore (a xxb)*c = |axxb| `
`rArr |(a_(1),a_(2),a_(3)),(b_(1),b_(2), b_(3)),(c_(1),c_(2),c_(3))|=|axxb|^(2)`