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

Step-by-step solution

Projection of v along u = Projection of w along u aligned & v u | u | = w u | u | & v u = w u ... (i) aligned Also, v and w are perpendicular to each other. v w =0... (ii) Now, | u - v + w |^2=| u |^2+| v |^2+| w |^2-2( u v )-2( v w )+2( u w ) | u - v + w |^2=1+4+9 | u - v + w |= 14