AP EAMCET202022 Sep 2020Evening ShiftMathematicsVector AlgebraActual
Let u and v be two vectors in R^2 . If | u + v |^2=2 (| u |^2+| v |^2 ) , then .....
Options
- Au = v
- Bu and v need not be same but they have same direction
- Cu and v need not be same but they have the opposite direction
- Du =2 v
Correct answer
A. u = v
Step-by-step solution
aligned & | u + v |^2=2 (|u|^2+|v|^2 ) &| u |^2+| v |^2+2 u v =2| u |^2+2| v |^2 &| u |^2+| v |^2=2 u v &| u |^2+| v |^2-2 u v=0 &( u - v )^2=0 & u - v =0 & u = v aligned Hence, option (1) is correct.