Statement 1 : Points `A(1,0),B(2,3),C(5,3),a n dD(6,0)` are concyclic. Statement 2 : Points `A , B , C ,a n dD` form an isosceles trapezium or `A Ba n dC D` meet at `Edot` Then `E A*E B=E C*E Ddot`

If the points (a, 0), (b,0), (0, c) , and (0, d) are concyclic (a, b, c, d > 0) , then prove that ab = cd .

If D , E ,a n dF are three points on the sides B C ,A C ,a n dA B of a triangle A B C such that A D ,B E ,a n dC F are concurrent, then show that BD*CE*AF=DC*EA*FB .

Let's plot the points A (4,0), B(0,6), C (2,5), D(7,1) E (?, 5) and F(?,5) on a graph sheet.

Let A(1,1,1),B(2,3,5)a n dC(-1,0,2) be three points, then equation of a plane parallel to the plane A B C which is at distance 2units is

Statement 1:Let A( vec a),B( vec b)a n dC( vec c) be three points such that vec a=2 hat i+ hat k , vec b=3 hat i- hat j+3 hat ka n d vec c=- hat i+7 hat j-5 hat kdot Then O A B C is a tetrahedron. Statement 2: Let A( vec a),B( vec b)a n dC( vec c) be three points such that vectors vec a , vec ba n d vec c are non-coplanar. Then O A B C is a tetrahedron where O is the origin.

Given three points are A(-3,-2,0),B(3,-3,1)a n dC(5,0,2)dot Then find a vector having the same direction as that of vec A B and magnitude equal to | vec A C|dot

Statement 1: If A ,B ,C are matrices such that |A_(3xx3)|=3,|B_(3xx3)|=-1,a n d|C_(2xx2)|=_2, t h e n|2A B C|=-12. Statement 2: For matrices A ,B ,C of the same order, |A B C|=|A||B||C|dot

If the vectors vec a , vec b ,a n d vec c form the sides B C ,C Aa n dA B , respectively, of triangle A B C ,t h e n

Statement 1: Distance of point D( 1,0,-1) from the plane of points A( 1,-2,0) , B ( 3, 1,2) and C( -1,1,-1) is 8/sqrt229 Statement 2: volume of tetrahedron formed by the points A,B, C and D is sqrt229/ 2

Statement 1: For a singular square matrix A ,A B=A C B=Cdot Statement 2; |A|=0,t h e nA^(-1) does not exist.