u , v , w are three vectors such that | u |=1 , | v |=2,| w |=3 . If the projection of v along u is equal to projection of w along u and v , w are perpendicular to each other, then | u - v + w |=

Step-by-step solution

| u |=1,| v |=2,| w |=3 According to the given condition, (Projection of v along u ) =( Projection of w along u ) array ll & v u | u | = w u | u | & v u = w u & ( w - v ) u =0 array Now consider, | u - v + w |= | u + w - v |^2 aligned & = | u |^2+| w - v |^2+2 u ( w - v ) & = (1)^2+| w - v |^2+0 & = 1+| w |^2+| v |^2-2( w v ) & = 1+9+4+0 aligned [ w and v are perpendicular ] = 14