The position vectors of points A and B are OA=q21 vector a and OB = q21 vector b .A point M is on AB such that AM = ½AB and a point N is on OB such that ON:NB= 1:

Question

The position vectors of points A and B are OA=  and OB =   .A point M is on AB such that AM = ½AB and a point N is on OB such that ON:NB= 1:3.  

Find:  

1. AB 
2. NM; 
3. lNMl, correct to 1 decimal place. 
4.  A translation vector maps A onto A'(5,−1). Find the coordinates of the image of B under the translation vector.  

Answer 1

 

1. AB= (−2) + (12 ) = (10 )
          (−4)     (−4)    ( −8)
2. 
   
3. 
   
           =√17
           =4.123
           ≈4.1
4. T=A⁻¹−A
   
   ∴ B¹(15,−9)