If a =2 i -5 j +8 k , b =7 i -5 j +3 k are two vectors and (2 a -3 b ) (4 a + b )=x i +y j +z k , then x+y+z=

Step-by-step solution

aligned & a =2 i -5 j +8 k , b =7 i -5 j +3 k & (2 a -3 b ) (4 a + b )=x i + y j + z k aligned aligned & 2 a -3 b =-17 i +5 j +7 k & 4 a + b =15 i -25 j +35 k aligned Now, (2 a -3 b ) (4 a + b )= | array ccc i & j & k -17 & 5 & 7 15 & -25 & 35 array | aligned & = i (175+175)- j (-595-105)+ k (25 17-75) & (2 a -3 b ) (4 a + b )=350 i +700 j +350 k aligned From eqns. (i) & (ii) aligned & x=350, y=700 & z=350 & x+y+z=350+700+350=140 aligned