A vector perpendicular to the plane containing the points A(1,-1,2), B(2,0,-1), C(0,2,1) is

Step-by-step solution

We know that a vector perpendicular to the plane containing the points A , B , C is given by A B + B C + C A We have, A = i - j +2 k , B =2 i +0 j - k and C =0 i +2 j + k Now, A B = | array ccc i & j & k 1 & -1 & 2 2 & 0 & -1 array |= i +5 j +2 k aligned B C =& | array ccc i & j & k 2 & 0 & -1 0 & 2 & 1 array |=2 i -2 j +4 k C A =& | array ccc i & j & k 0 & 2 & 1 1 & -1 & 2 array |=5 i + j -2 k Thus, A B + B C + C B =( i +5 j +2 k ) & +(2 i -2 j +4 k )+(5 i + j -2 k ) =& 8 i +4 j +4 k aligned