Consider the vectors x = i +2 j +3 k , y =2 i +3 j + k , and z =3 i + j +2 k For two distinct positive real numbers and , define X = x + y - z , Y = y + z - x , and Z = z + x - y If the vectors X , Y , and Z lie in a plane, the value of + -3 is ______ .
A. A
| array ccc & & -1 \\ -1 & & \\ & -1 & array | | array ccc 1 & 2 & 3 \\ 2 & 3 & 1 \\ 3 & 1 & 2 array | _ -0 =0 aligned & ( ^3+ ^3-1 )-(- - - )=0 \\ & ^3+ ^3+3 =1 \\ & ^3+ ^3+(-1)^3=3( )( )(-1) \\ & + -1=0 aligned So, + -3=-2
Related: Mathematics — Vector Algebra · All PYQ Banks