AP EAMCET202123 Aug 2021Morning ShiftMathematicsVector AlgebraActual
Let u and v be two vectors. Then |u-v|=|| u|-| v|| if and only if
Options
- A|u|=|v|
- Bu and v have the same direction
- Cu and v have the opposite direction
- Du=v
Correct answer
B. u and v have the same direction
Step-by-step solution
Since, |u-v|^2=|u|^2+|v|^2-2 u v and | u|-| v||^2=|u|^2+|v|^2-2| u || v | Now, |u-v|^2= .|| u|-| v |^2 only, when It only happens when u and v have same direction. aligned u v & =| u || v | | u | | v & =| u || v | =1 & =0 aligned