Let `L_1 and L_2` be two lines intersecting at P If `A_1,B_1,C_1` are points on `L_1,A_2, B_2,C_2,D_2,E_2` are points on `L_2` and if none of these coincides with P, then the number of triangles formed by these 8 points is

Let l_(1) and l_(2) be thw two lines intersecting at P. If A_(1), B_(1), C_(1) are points on l_(1), A_(2), B_(2), C_(2), D_(2), E_(2) are points on l_(2) an dif none of these coincides with P, then the number of triangles formed by joining these eight points is-

Let l_(1) and l_(2) be the two skew lines. If P, Q are two distinct points on l_(1) and R, S are two distinct points on l_(2) , then prove that PR cannot be parallel to QS.

Let l_(1) and l_(2) be the two skew lines. If P, Q are two distinct points on l_(1) and R, S are two distinct points on l_(2) , then prove that PR cannot be parallel to QS.

Consider three planes P_1 : x-y + z = 1, P_2 : x + y-z=-1 and P_3 : x-3y + 3z = 2 Let L_1, L_2 and L_3 be the lines of intersection of the planes P_2 and P_3, P_3 and P_1 and P_1 and P_2 respectively.Statement 1: At least two of the lines L_1, L_2 and L_3 are non-parallel The three planes do not have a common point

Consider three planes P_1 : x-y + z = 1 , P_2 : x + y-z=-1 and P_3 : x-3y + 3z = 2 Let L_1, L_2 and L_3 be the lines of intersection of the planes P_2 and P_3 , P_3 and P_1 and P_1 and P_2 respectively.Statement 1: At least two of the lines L_1, L_2 and L_3 are non-parallel The three planes do not have a common point