Prove that `AB bot CD` if A = (2, 1), B = (0, -1), C= (-1, 8), D = (4, 3)

Prove that AB||CD if A = (-1,-2), B = (0, 1), C = (3, 0), D = (2, -3)

The area of the quadrilateral ABCD, where A (0, 4, 1), B (2, 3, - 1), C(4, 5, 6) and D (2, 6, 2) is equal to :

The points A (4,5,1), B (0,-1,-1), C(3,9,4) and D(-4,4,4) are

Prove that (AB)^(-1) = B^(-1) . A^(-1) give that A = [(2,3),(1,-4)] and B = [(1,-2),(-1,3)] .

From the sets given below, select equal sets : A = { 2, 4, 8, 12}, B = { 1, 2, 3, 4}, C = { 4, 8, 12, 14}, D = { 3, 1, 4, 2} E = {–1, 1}, F = { 0, a}, G = {1, –1}, H = { 0, 1}

Prove that the points A(0,-1),B(-2,3),C(6,7) and D(8,3) are the vertices of a rectangle ABCD .

Without expanding the determinant, prove that {:|( a, a ^(2), bc ),( b ,b ^(2) , ca),( c, c ^(2) , ab ) |:} ={:|( 1, a^(2) , a^(3) ),( 1,b^(2) , b^(3) ),( 1, c^(2),c^(3)) |:}

Prove that abs{:(a^(2) + 1, ab , ac),(ab, b^(2) + 1, bc),(ca, cb, c^(2) +1):}=1 + a^(2) + b^(2) +c^(2)

Show that the points A(-1,4,-3), B(3,2,-5) C(- 3,8,-5) and D (-3,2,1) are coplanar