If ` | vec A | =2 and | vec B| =4`, then match the relations in column I with the angle` theta` between ` vec A and vec B` in column II.
Column I, Column II
(a) ` |vec A xx vec B| =0` , (i) ` theta =30^@`
(b) `| vec A xx vec B|=0` , (ii) ` theta =45^@`
(c ) ` vec A xx vec B| =4` , (iii) ` theta =90^@`
(d) ` | vec A xxx vec B| = 4 sqrt 2` , (iv) ` theta =0^@`.

Explanation

Given |A|=2 and |B|=4
(a) `|AxxB|=AB sin theta =0 " " rArr " " 2xx4xxsin theta=0`
`rArr " " sin theta =0 = sin 0^(@)" " rArr " " theta=0^(@)`
`:.` Option (a) matches with option (iv).
(b) `|AxxB|=AB sin theta=8 " " rArr " " 2xx4sin theta=8`
`rArr " " sin theta =1=sin 90^(@) " " rArr " " theta=90^(@)`
`:.` Option (b) matches with option (iii).
(c) `|AxxB|=AB sin theta =4 " " rArr " " 2xx4sin theta=4`
`rArr sin theta =(1)/(2)=sin 30^(@) " " rArr " " theta=30^(@)`
`:.` Option (c) matches with option (i).
(d) `|AxxB|=ABsin theta=4sqrt(2) " " rArr " " 2xx4 sin theta = 4 sqrt(2)`
`rArr " " sin theta =(1)/(sqrt(2))=sin 45^(@) " " rArr " " theta=45^(@)`
`:.` Option (d) matches with option (ii).