The magnitude of the projection of the vector 2 i + j + k on the vector perpendicular to the plane containing the vectors i + j + k and i +2 j +3 k is

Step-by-step solution

The vector perpendicular to both vectors containing ( i + j + k ) and ( i +2 j +3 k ) is aligned & =( i + j + k ) ( i +2 j +3 k ) & = | array lll i & j & k 1 & 1 & 1 1 & 2 & 3 array | & = i -2 j + k aligned Therefore, the magnitude of the projection of vector (2 i + j + k ) on ( i -2 j + k ) is aligned & = | (2 i + j + k )( i -2 j + k ) 1^2+(-2)^2+(1)^2 | & = | 2-2+1 6 | & = 1 6 aligned