1.

If veca, vecb and vecc are three units vectors equally inclined to each other at an angle alpha. Then the angle between veca and plane of vecb and vecc is

Answer»

`theta=cos^(-1)(cosalpha)/(cosalpha/2)`
`theta=sin^(-1)(cosalpha)/(cosalpha/2)`
`theta=cos^(-1)(sinalpha/2)/(sinalpha)`
`theta=sin^(-1)(sinalpha/2)/(sinalpha)`

Solution :LET `vec(OA)=VECA, vec(OB)=vecb, vec(OC)=vecc`
Then from the given conditions
`veca.veca+(vecb-vecc).(vecb-vecc)=vecb.vecb+(vecc-veca).(vecc-veca)`
`RARR vecc.(vecb-veca)=0`
`rArr vec(BA).vec(OC)=0`
Hence `AB bot OC`. Similarly,
`BC bot OA` and `CA bot OB`


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