Question

Sa se determine m astfel incat vectorii u=(m+5)i+(2m+1)j si v=(2m-3)i+(m-3)j sa aiba acelasi modul.

Answer 1

u=(m+5)i+(2m+1)j si v=(2m-3)i+(m-3)j

|u| = |v|

=> √[(m+5)²+(2m+1)²] = √[(2m-3)²+(m-3)²]

=> (m+5)²+(2m+1)² = (2m-3)²+(m-3)²

=> m²+10m+25+4m²+4m+1 =

= 4m²-12m+9+m²-6m+9

=> 10m+25+4m+12m+6m-18 = 0

=> 32m+7 = 0 => 32m = -7 => m = -7/32