Question

已知向量a=(cos3π/2,sin3π/2),向量OA=向量a-向量b,向量OB=向量a+向量b ,若△OAB是以O为

Answer 1

|OA|= |a-b| = |OB| = |a+b|

=> (a-b).(a-b) = (a+b).(a+b)

=> a.b =0

|a|^2 = (cos3π/2)^2+(sin3π/2)^2 =1

|a| =1

△OAB是以O为直角

=> (a+b).(a-b)=0

=> |a| =|b|=1

|OA|^2 = |a|^2+|b|^2 = 2

|OB|^2 = |OA|^2 = 2

△OAB的面积

= (1/2)|OA||OB|

=1

Ans:A