If with reference to a right handed system of mutually perpendicular unit vectors ` hat i ,\ hat j ,\ hat k` we have ` vecalpha=3 hat i- hat j ,\ a n d\ vecbeta=2 hat i+ hat j-3 hat kdot` Express ` vecbeta` in the form ` vecbeta= vecbeta_1+ vecbeta_2,\ w h e r e\ vecbeta_1` is parallel to ` vecalpha\ a n d\ vecbeta_2` is perpendicular to ` vecalphadot`

Answer

`vecbeta = ((3)/(2) hati - (1)/(2) hatj) +((1)/(2) hati + (3)/(2) ahtj + 3 hatk)`