**Find two vectors v1 and v2 whose sum is −4−5 , where v1 is parallel to 0−5 while v2 is perpendicular to 0−5**

**Answer:**

v1=r(0,-5) =>v1 is parallel to (0,-5)

v1+v2=(-4,-5)=> sum of v1 and v2

v2=(-4,-5)-r(4,-2)=> subtract v1

v2=(-4-4r,-5+2r)=> v2

v2•(0,-5)=0 => v2 is perpendicular to (0,-5)

(-4-4r,-5+2r)•(0,-5)=0 => we found v2 in the previous calculations

25-10r=0 => solve for r

10r=25

r=5/2

v1=r(0,-5)=(0,-25/2)=> find v1 by replacing r with 5/2

v2=(-4-4r,-5+2r)=(-14,0)=> find v2 by replacing r with 5/2

v1=r(0,-5)=(0,-25/2)

v2=(-4-4r,-5+2r)=(-14,0)