In A B C if A( ), B( ) and C( ) are the position vectors of the vertices, then the length of the perpendicular from A to B C is

Step-by-step solution

Let A B C be a triangle and , , be the position vector of the vertices A, B, C respectively. Let A M be the perpendicular from A to B C Then, Area of A B C aligned & = 1 2 (B C) (A M) & = 1 2 | B C || A M | aligned Area of A B C = 1 2 | + + + | array lrl & 1 2 | B C || A M |= 1 2 | + + | & | A M |= | + + | | - | array