Two planes` P_1 and P_2` pass through origin. Two lines `L_1 and L_2` also passingthrough origin are such that ` L_1` lies on `P_1` but not on `P_2, L_2` lies on `P_2` but not on `P_1 A,B, C` are there points other than origin, then prove that the permutation `[A', B', C']` of `[A, B, C]` exists. Such that:

Two planes P_(1) and P_(2) pass through origin. Two lines L_(1) and L_(2) also passingthrough origin are such that L_(1) lies on P_(1) but not on P_(2),L_(2) lies on P_(2) but not on P_(1)A,B,C are there points other than origin,then prove that the permutation [A',B',C'] of [A,B,C]^(2) exists.Such that:

The direction cosines of the line passing through P(2,3,-1) and the origin are

If lines l_(1), l_(2) and l_(3) pass through a point P, then they are called…………. Lines.

Consider two lines L_1a n dL_2 given by a_1x+b_1y+c_1=0a n da_2x+b_2y+c_2=0 respectively where c1 and c2 !=0, intersecting at point PdotA line L_3 is drawn through the origin meeting the lines L_1a n dL_2 at Aa n dB , respectively, such that PA=P B . Similarly, one more line L_4 is drawn through the origin meeting the lines L_1a n dL_2 at A_1a n dB_2, respectively, such that P A_1=P B_1dot Obtain the combined equation of lines L_3a n dL_4dot

A point P lies on a line whose ends are A(1,2,3) and B(2,10,1). If z-coordinate of P is 7 then point P is

If a plane has intercepts a,b,c on axes and is at a distance of p units from the origin then prove that 1/a^2+1/b^2+1/c^2=1/p^2

P_(1) : x + 3y - z = 0 and P_(2) : y + 2z = 0 are two intersecting planes P_(3) is a plane passing through the point (2,1,-1) and through the line of intersection of P_(1) and P_(2) Distance of P_(3) from origin is _______ units.