The angles of triangle, two of whose sides are represented by vectors `sqrt(3)( vec axx vec b) \a n d \ vec b-( hat adot vec b) hat a ,w h e r e vec b` is a non zero vector and ` hat a` is unit vector in the direction of ` vec a ,` are

Options

A. `tan ^(-1)(sqrt3)`
B. `tan ^(-1)(1//sqrt3)`
C. `cot^(-1)(0)`
D. tant^(-1)(1)`

Answer

a,b,c

Explanation

consider `vecV_(1). vecV_(2) = 0 Rightarrow A = 90^(@)`
using the sine law, `|(vecb-(veca.vecb)hata)/sin theta| = (sqrt3|hataxxvecb|)/costheta`

`or tan theta = 1/sqrt3 (|vecb - (hata xx vecb) hata|)/(|hata xx vecb|)`
`1/sqrt3(|(hataxxvecb)xxhata|)/(|hata xx vecb|)`
`1/sqrt3 (|hata xxvecb||hata|sin90^(@))/(|hataxx vecb|) = 1/sqrt3`
`or theta pi/6`