Evaluate `Delta = |{:(3, 4, 5), (-6, 2, -3), (8, 1, 7):}|`

If Delta = |{:(1,2,3),(2,3,5),(3,6,12):}|and Delta' = |{:(4,8,15),(3,6,12),(2,3,5):}| , then

Find the lengths of the medians of the triangle whose vertices are A (2,-3, 1), B (-6,5,3), C(8,7,- 7).

If (1, 1, 1) is the centroid of the triangle with vertices (2a, 3, 7), (-4, 3b, -8) and (8, 4, 6c), find a, b, c.

If (1, 1, 1) is the centroid of the triangle with vertices (2a, 3, 7), (-4, 3b, -8) and (8, 4, 6c), find a, b, c.

Find the area of the triangle with vertices at the points: (i) (3, 8), (-4, 2) and (5, -1) (ii) (2, 7), (1, 1) and (10, 8)

Find the point of intersection of the medians of the triangle with vertices (-1, -3, 4), (4, -2,-7), (2, 3, -8).

Find minors of element 6 in the determinant Delta=|[ 1, 2, 3],[ 4, 5, 6],[ 7 , 8, 9]|

If ( - 4 , 7 , 5) , ( 2 , - 6 , - 3) and ( 8 , 2 , - 5) are the coordinates of the mid-points of the sides of a triangle, then find the coordinates of the centroid of the triangle.

Find the minor of 1 in the determinant Delta=|[3, 4, 5 ],[2, 7, 1],[ 9, 2, 6]|