Question

If ` | vec A | =2 and | vec B| =4`, then match the relations in column I with the ange ` 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^@`.

Answer 1

Here ` A= 2 and B=4`.
`(a) | vec A xx vec B| =0 = AB sin theta =2 xx 4 sin theta or =0 and theta =0^@`. It matches with option (iv).
`(b) | vec A xx vec B| =8 = AB sin theta 2 xx 4 sin theta or sin theta =1 and theta =90^@`. It matches with option (iii).
`(c ) | vec A xx vec B| =4 =2 xx 4sin theta or sin theta =1/2 or theta =30^@`. It matches with option (i).
`(d) | vec A xx vec B| = 4 sqrt 2=2 xx 4 or sin theta =1 /(sqrt 2) or theta =45^@`. It matches with option (ii).