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If | vec A | =2 and | vec B| =4, then ...

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^@`.

Text Solution

Verified by Experts

(a) `|vec AxxvecB|=0`
`AB sin theta =0`
`2xx4 sin theta=0`
`rArr theta =0^(@)`
(a) `rarr (iv)`
(b) `|vecAxxvecB|=8`
`AB sin theta =8`
`2xx4 sin theta =8`
`sin theta=1`
`rArr theta =90^(@)`
(b) `rarr (iii)`
(c) `|vecAxxvecB|=4`
`AB sin theta =4`
`2xx4 sin theta=4`
`sin theta =1//2`
`rArr theta =30^(@)`
(c) `rarr (i)`
(d) `|vecAxxvecB|=4 sqrt2`
`sin theta =(1)/(sqrt2)`
`rArr theta =45^(@)`
(d) `rarr (ii)`
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