Let `n_1, n_2, n_3, n_4` be vectors normal to the planes `p_1, P_2 P_3, P_4` respectively, then the vector perpendicular to the lines of intersection of `p_1 and p_2, and p_3 and p_4`, is

Let E_1, E_2, E_3…………,E_n be independent events with respective probability P_1,P_2,P_3,………….,P_n find the probability that none of them occurs.

( If the planes )/(r*n_(1))=p_(1),vec r.n_(2)=p_(2) and vec r.n_(3)=p_(3), have a common line of intersection then

Given that A_1,A_2,A_3, A_n are n points in a plane whose coordinates are x_1,y_1),(x_2,y_2) ,(x_n ,y_n), respectively. A_1A_2 is bisected at the point P_1,P_1A_3 is divided in the ratio A :2 at P_2,P_2A_4 is divided in the ratio 1:3 at P_3,P_3A_5 is divided in the ratio 1:4 at P_4 , and so on until all n points are exhausted. Find the final point so obtained.

Given that A_1,A_2,A_3, A_n are n points in a plane whose coordinates are x_1,y_1),(x_2,y_2) ,(x_n ,y_n), respectively. A_1A_2 is bisected at the point P_1,P_1A_3 is divided in the ratio A :2 at P_2,P_2A_4 is divided in the ratio 1:3 at P_3,P_3A_5 is divided in the ratio 1:4 at P_4 , and so on until all n points are exhausted. Find the final point so obtained.

Given that A_1,A_2,A_3, A_n are n points in a plane whose coordinates are x_1,y_1),(x_2,y_2) ,(x_n ,y_n), respectively. A_1A_2 is bisected at the point P_1,P_1A_3 is divided in the ratio A :2 at P_2,P_2A_4 is divided in the ratio 1:3 at P_3,P_3A_5 is divided in the ratio 1:4 at P_4 , and so on until all n points are exhausted. Find the final point so obtained.

Let A_1,A_2,A_3,...,A_n are n Points in a plane whose coordinates are (x_1,y_1),(x_2,y_2),....,(x_n,y_n) respectively. A_1A_2 is bisected at the point P_1,P_1A_3 is divided in the ratio 1:2 at P_2,P_2A_4 is divided in the ratio 1:3 at P_3,P_3A_5 is divided in the ratio 1:4 at P_4 and the so on until all n points are exhausted. find the coordinates of the final point so obtained.

If the three planes rcdotn_1=p_1, rcdotn_2=p_2 and rcdotn_3=p_3 have a common line of intersection, then p_1(n_2timesn_3)+p_2(n_3timesn_1)+p_3(n_1timesn_2) is equal to