If ` vec a , vec b , a n d harr c` are three unit vecrtors such that ` vec axx( vec bxx vec c)=1/1 vec b ,t h e n( vec ba n d vec c` being non-parallel`)` angle between ` vec aa n d vec b` is`pi//3` b.`"a n g l eb e t w e e n" vec aa n d vec c"i s"pi//3` c. a. angle between ` vec aa n d vec b` is`pi//2` d. a. angle between ` vec aa n d vec c` is`pi//2`

Options

A. angle between `veca and vecb is pi//3`
B. angle between `veca and vecc is pi//3`
C. angle between `veca and vecb is pi//2`
D. angle between `veca and vecc is pi//2`

Answer

b,c

Explanation

`vecaxx (vecb xxvecc) = 1/2 vecb`
`or (veca.vecc) vecb - (veca .vecb) vecc= 1/2 vecb`
` Rightarrow veca.vecc = 1/2 and veca.vecb=0`
` Rightarrow 1.1 cos alpha = 1/2 and veca bot vecb`
` Rightarrow alpha= pi/3 and veca bot vecb`