Let `veca , vecb and vecc` be unit vectors such that `veca+vecb+vecc=vecx, veca.vecx =1, vecb.vecx = 3/2 ,|vecx|=2` then find theh angle between `vecc and vecx`.

Explanation

`veca+vecb+vecc=vecx`
Taking dot with `vecx` on both sides, we get
`vecx.veca+vecx.vecb+vecx.vecc=vecx.vecx= |vecx|^(2)=4`
or ` 1+ 3/2 + vecx.vecc=4 or vecx.vecc = 3/2`
if `theta` is the angle between unit vectors `veca + vecb` . then
`|vecx||vecc|cos theta = 3//2`
` Rightarrow cos theta = 3//4 or theta = cos^(-1)(3//4)`