If the point P( , , ) lies on the plane 2 x+y+z=1 and [ ] [ array lll 1 & 9 & 1 8 & 2 & 1 7 & 3 & 1 array ]= [ array lll 0 & 0 & 0 array ] , then ^2+ ^2+ ^2=

Step-by-step solution

Point P( , , ) lies on plane 2 x+y+z=1 Form Eqs. (i) and (iv), we get 2 + + =1 + + =0 =1 put in Eqs. (ii) and (iii), we get 1+8 +7 =0 and 9(1)+2 +3 =0 aligned Eq (V) -4 Eq. (vii) & 8 +7 & =-1 8 +12 & =-36 & =-1 -5 & =35 & =-7 aligned Put value of in Eqs. (vi), we get 2 +3(-7)=-9 2 =12 =6 Now, ^2+ ^2+ ^2 =(1)^2+(6)^2+(-7)^2=1+36+49=86