If p is the perpendicular distance from origin to the plane passing through (1,0,0),(0,1,0) and (0,0,1) , then what is 3 p^2 equal to?

Step-by-step solution

Plane passing through (1,0,0),(0,1,0) and (0,0,1) a = i , b = j , c = k Let, r =x i +y j +z k aligned & ( r - a ) [( b - a ) ( c - a )]=0 & aligned b - a & = j - i and c - a = k - i ( b - a ) ( c - a ) & = | array ccc i & j & k -1 & 1 & 0 -1 & 0 & 1 array |= i j k ( r - a ) & =(x i +y j +z k )-( i ) & =(x-1) i +y j +z k aligned aligned We have, aligned [(x-1) i +y j +z k ] ( i + j + k ) & =0 & (x-1)+y+z=0 aligned Equating of plane x+y+z-1=0 distance from origin to the plane = |-1| (1)^2+(1)^2+(1)^2 = 1 3 unit align