If ` vec a , vec ba n d vec c` are the position vectors of the vertices `A ,Ba n dC` respectively, of ` A B C ,` prove that the perpendicular distance of the vertex `A` from the base `B C` of the triangle `A B C` is `(| vec axx vec b+ vec bxx vec c+ vec cxx vec a|)/(| vec c- vec b|)dot`

Explanation

`|vec(BC)xxvec(BA)|=|vecaxxvecb+vecb+vecbxxvecc+veccxxveca|`
`|vec(BC)||vec(BA)|sin B=|vecaxxvecbxxvecbxxvecc+veccxxveca|`
`|vecc-vecb| (ABsinB)=|vecaxxvecb+vecbxxvecc+veccxxveca|`
Therefore, the length of perpendicualr from A on BC is
`AL=ABsinB=(|vecaxxvecb+vecbxxvecc+veccxxveca|)/(|vecb-vecc|)`