The coordinates of the vertices of the triangle are A(-2,3,6), B(-4,4,9) and C(0,5,8) . The direction cosines of the median BE are

Step-by-step solution

The median BE connects vertex B to the midpoint E of side AC. The coordinates of A are (-2, 3, 6) and C are (0, 5, 8) . The midpoint E of AC is given by E = ( -2 + 0 2 , 3 + 5 2 , 6 + 8 2 ) = (-1, 4, 7) . The vector BE is given by E - B = (-1 - (-4), 4 - 4, 7 - 9) = (3, 0, -2) . The magnitude of vector BE is | BE | = 3^2 + 0^2 + (-2)^2 = 9 + 0 + 4 = 13 . The direction cosines of the vector BE are obtained by dividing the components of the vector by its magnitude: ( 3 13 , 0 13 , -2 13 ) = ( 3 13 , 0, - 2 13 ) . Ans