If `theta` is the abgle between two vectors A and B , then match the following two columns.
`{:(,"Column I ",,"Column II"),((A),A.B=|AxxB|,(P),theta=90^(@)),((B),A.B=B^(2),(Q),theta=0^(@)or 180^(@)),((C),|A+B|=|A-C|,(r),A=B),((D), |AxxB|=AB,(s),"None"):}`

Options

A. `Atos,Btoq,Cto p,Dto p`
B. `Ato p,Btoq,Cto p,Dto p`
C. `Atoq,Btoq,Ctor,Dtos`
D. `Ato p,Btor,Ctor,Dtos`

Answer

A

Explanation

i. `A.B=ABcostheta`
`|AxxB|=ABsintheta`
`A.B=|AxxB|`
Only when, `theta=45^(@)`
ii. `A.B=B^(2)`
When `A=BorA.B=ABcostheta`
`theta=0ortheta=180^(@)`
iii.`|A+B|=sqrt(A^(2)+B^(2)-2ABcostheta)`
`|A-B|=sqrt(A^(2)+B^(2)-2ABcostheta)` when `theta=90^(@)1`
`|A+B|=|A-B|`
iv. When `theta90^(@)`
then `|AxxB|=AB`