We suppose in R^2 the base (i^→ ;j^→ ).
we have these vectors:
u^→ =(m^2 −m)i^→ +2mj^→ ;
v^→ =(m−1)i^→ +(m+1)j^→ m ∈ R^∗
1)Determinate m for which the system
(u^→ ;v^→ ) is linear dependant( det(u^→ ;v^→ )=0)
A train which travels at a uniform speed due to mechanical fault after
traveling for an hour goes at 3/5 th of the original speed and reaches the
destination 2 hours late. If the fault occured after traveling another 50
miles the train would have reached 40 minutes earlier. What is the
distance between the two stations ?