A,B,C and d are four points in a plane with position vectors `overset(to)(a),overset(to)(b),overset(to)(c )` and `overset(to)(d)` respectively such that `(overset(to)(a)-overset(to)(d)).(overset(to)(b)-overset(to)(c))=(overset(to)(b)-overset(to)(d))(overset(to)(c)-overset(to)(a))=0` The point D then is the .... of the `DeltaABC`

Answer

Orthocentre

Explanation

As `(vec(a) - vec(d)) . (vec(b) -vec(c )) = (vec(b) -vec(d)) . (vec(c )-vec(a)) =0`
`rArr AD bot BC "and " BD bot CA`
which clearly represents from figure that D is orthocentre of `DeltaABC`