if `vecr=xhati+yhatj+zhatk` find `(vecr xx hati).(vecr xx hatj)+xy`

If vecr=xhati+yhatj+zhatk , find : (vecrxxhati)*(vecrxxhatj)+xy .

If vecr=xhati+yhatj+zhatk , find : (hatrxxhati)*(hatrxxhatj)+xy .

The angle between the planes vecr. (2 hati - 3 hatj + hatk) =1 and vecr. (hati - hatj) =4 is

The angle between the planes vecr. (2 hati - 3 hatj + hatk) =1 and vecr. (hati - hatj) =4 is

For any vector vecr = xhati+yhatj+zhatk , prove that vecr = (vecr.hati)hati+(vecr.hatj)hatj+(vecr.hatk)hatk .

The solution vectors vecr of the equation vecr xx hati=hatj+hatk and vecr xx hatj=hatk+hatj represent two straight lines which are :