Let u, v and w are non-coplanar vectors, then the value of (u+2 v-w) [(u-v) (u-v-w)] [u v w]

Step-by-step solution

Given u, v and w are non coplanar vectors. To Find The value of (u+2 v-w) [u-v) (u-v-w)] [u v w] aligned & (u+2 v-w) [u u-u v-u w & -v u+v v+v w] [u v w] & aligned aligned & = (u+2 v-w) [0-u v-u w+u v+0+v w] [u v w] & u (-u w)+u (v w)-2 v(u w)+2 v (v w) & = +w (u w)-w (v w) [u v w] & aligned aligned & - [ array lll u & u & w array ]+ [ array lll u & v & w array ]-2 [ array lll v & u & w array ]+2 [ array lll v & v & w array ] & = +[w u w]-[w w] [u v w] & = [u w]+2[u w] [u w] [u u w]=[v w] & aligned aligned & .= [ a